Encyclopedia of
Nanoscience and
Nanotechnology
www.aspbs.com/enn
Nanotubes for Nanoelectronics
Zhi Chen
University of Kentucky, Lexington, Kentucky, USA
CONTENTS
1. Introduction
2. Progress in Nanoelectronics Prior
to Nanotubes
3. Synthesis and Electrical Properties
of Carbon Nanotubes
4. Single-Electron Transistors
5. Field-Effect Transistors, Logic Gates,
and Memory Devices
6. Doping, Junctions, and Metal–Nanotube
Contacts
7. Nanotube-Based Nanofabrication
8. Summary
Glossary
References
1. INTRODUCTION
Carbon nanotubes (CNTs) have emerged as a viable electronic material for molecular electronic devices because of
their unique physical and electrical properties [1–7]. For
example, nanotubes have a lightweight and record-high elastic modulus, and they are predicted to be by far the strongest
fibers that can be made. Their high strength and high flexibility are unique mechanical properties. They also have amazing
electrical properties. The electronic properties depend drastically on both the diameter and the chirality of the hexagonal
carbon lattice along the tube [8–10].
Carbon nanotubes were discovered by Iijima in 1991 at
the NEC Fundamental Research Laboratory in Tsukuba,
Japan [1]. Using a transmission electron microscope (TEM),
he found carbon tubes consisting of multiple shells (see
Fig. 1). These early carbon tubes are called multiwall nanotubes (MWNTs). Since then, extensive research has been
focused on synthesis and characterization of carbon nanotubes. In 1993, Ijima’s group [11] and Bethune et al. [12]
at IBM Almaden Research Center at San Jose, California, synthesized carbon nanotubes with a single shell, called
single-wall nanotubes (SWNTs). Because of their simple and
well-defined structure [13], the single-wall nanotubes serve
ISBN: 1-58883-001-2/$35.00
Copyright © 2004 by American Scientific Publishers
All rights of reproduction in any form reserved.
as model systems for theoretical calculations and for critical
experimental studies. Since then, the physical and electrical
properties of carbon nanotubes have been studied extensively. Only a few years ago, people began to utilize carbon
nanotubes’ unique electrical properties for electron device
applications. Up to now, there has been no extensive review
to cover the progress in nanoelectronic devices using carbon
nanotubes.
In this chapter, I aim to present extensive review on
progress in electronic structure and transport properties of
carbon nanotubes and nanoelectronic devices based on carbon nanotubes ranging from quantum transport to fieldeffect transistors. This chapter is organized as follows. It
begins with brief review of the progress in micro- and nanoelectronic devices prior to carbon nanotubes (Section 2).
Then the synthesis and physical properties of carbon nanotubes will be discussed in Section 3. Nanoelectronic devices
based on carbon nanotubes including single-electron transistors (SETs), field-effect transistors, logic gates, and memory
devices will be reviewed in Sections 4 and 5. The chemical doping, junctions, and metal–nanotube contacts will be
described in Section 6. Finally, nanofabrication based on
carbon nanotubes including controlled growth and selective placement of nanotubes on patterned Si substrates will
be reviewed in Section 7. Since the discovery of carbon
nanotubes, over 1000 papers on carbon nanotubes have
been published. It is unlikely that every paper will be
included in this chapter, because most papers dealt with synthesis, physical, and chemical properties of nanotubes. In
this chapter, I will focus on electrical properties of nanotubes, nanoelectronic devices constructed with nanotubes,
and nanotube-based nanofabrication.
2. PROGRESS IN NANOELECTRONICS
PRIOR TO NANOTUBES
In 1959 Richard Feynman delivered his famous lecture,
“There is Plenty of Room at the Bottom.” He presented a
vision of exciting new discoveries if one could fabricate materials and devices at the atomic and molecular scale. It was
not until 1980s that instruments such as scanning tunneling microscopes (STM), atomic force microscopes (AFM),
and near-field microscopes were invented. These instruments
Encyclopedia of Nanoscience and Nanotechnology
Edited by H. S. Nalwa
Volume 7X: Pages (919-942)
(1–24)
920
2
Nanotubes for Nanoelectronics
a
b
c
Proof's Only
on the surfaces of materials [17]. Later the STM was used to
modify surfaces at the nanometer scale and the manipulation and positioning of single atoms on surface was achieved
[18]. In 1993, Crommie et al. [19] eloquently demonstrated
with a “quantum corral” where the STM can be used not
only to characterize the electronic structure of materials on
a truly quantum scale, but also to modify this quantum structure. This suggested that the STM and AFM might be used
for atom-by-atom control of materials modification, leading
to atomic resolution. This potential motivated researchers to
attempt to use STM and AFM for nanolithography [20–25].
This task has not been easy due to the irreproducibility
of the modifications, the slow “write” speed, and the difficulty of transferring such fine manipulations into functioning
semiconductor devices [21]. Until now, reliable fabrication
and robust pattern transfer for linewidths below 10 nm has
not been achieved yet.
2.2. Metal-Oxide-Semiconductor
Field-Effect Transistors
Figure 1. Cross-section images of carbon nanotubes by a highresolution TEM. Reprinted with permission from [1], S. Iijima, Nature
354, 56 (1991). © 1991, Macmillan Publishers Ltd.
provide “eyes” and “fingers” required for nanostructure
measurement and manipulation [14]. The driving force for
nanoelectronics is the scaling of microelectronic devices to
nanoscale, which is the engine for modern information revolution. The microelectronics revolution began in 1947 when
John Bardeen, Walter H. Brattain, and William Shockley of
Bell Telephone Laboratories invented the first solid state
transistor, the Ge point-contact transistor [15]. Solid state
transistors had far superior performance, much lower power
consumption, and much smaller size than vacuum triodes.
People began to produce individual solid state components
to replace the vacuum tubes in circuits in a few years after
the invention. In 1958, Jack Kilby of Texas Instruments conceived a concept for fabrication of the entire circuit including components and interconnect wires on a single silicon
substrate [16]. In 1959, Robert Noyce of Fairchild Semiconductor individually conceived a similar idea [15]. This
concept has evolved into today’s very-large-scale integrated
circuits or “microchips,” which consist of millions of transistors and interconnect wires on a single silicon substrate. The
major driving force for this revolutionary progress is miniaturization of transistors and wires from tens of micrometers
in the 1960s to today’s tens of nanometers. The scaling
down of transistor and interconnect wires led to more and
more transistors being incorporated into a single silicon
chip, resulting in faster and more powerful computer chips.
With the success in microelctronics and of the semiconductor industry, it is natural to consider extending the micrometer size devices to nanometer size devices.
2.1. STM/AFM-Based Nanofabrication
There was not much progress in nanoelectronics until the
1980s. In 1981, the scanning tunneling microscope, invented
by G. K. Binnig and H. Rohrer of IBM Zurich Research
Laboratory, produced the first images of individual atoms
As early as the 1920s and 1930s, a concept for amplifying devices based on the so-called field effect was proposed with little understanding of the physical phenomena
[26, 27]. After 30 years, the field-effect transistor based on
the SiO2 /Si structure finally became practical [28]. Since that
time, the metal-oxide-semiconductor field-effect transistor
(MOSFET) has been incorporated into integrated circuits
and has grown to be the most important device in the semiconductor industry ranging from memory chips, microprocessors, and many other communication chips. Figure 2a
shows the structure of an n-channel MOSFET. It consists
of p-type Si, heavily doped n+ source and drain, and an
insulated gate. When the gate voltage is zero, the region
underneath the gate oxide is p-type. There are two pn+ junctions near the source and the drain. When applying a voltage
across the source and the drain, either of the two pn+ junctions is reverse biased. Thus the transistor conducts no current. When the gate voltage is larger than zero but less than
its threshold voltage, depletion happens underneath the gate
oxide, which is still not conductive. When the gate voltage is
larger than its threshold voltage, an inversion layer (n-type)
is induced underneath the gate oxide, which forms a conduction channel connecting both source and drain. Thus the
transistor conducts current. The typical I–V curves for an
n-MOSFET with a gate length of 0.25 m and a width of
15 m are shown in Figure 2b. The driving force behind this
(a)
VS
(b)
Source
VG
Gate Si2O
n+
VD
Drain
n+
Inversion
P-Si
3.5 V
8
3V
6
2.5 V
4
Depletion
VB
ID(mA)
10
2V
2
0
VGS=1.5 V
0
1
2
3
4 V (V)
DS
Figure 2. (a) Schematic structure of a Si MOSFET used in various
microchips for digital signal processing and (b) its current–voltage
characteristics.
921
3
Nanotubes for Nanoelectronics
remarkable development is the cost reduction and performance enhancement of integrated circuits (ICs) due to the
continuous miniaturization of transistors and interconnect
wires. The continuous scaling of transistors and the increase
in wafer size has been and will continue to be the trend
for the semiconductor industry. The transistor gate length
(feature size) has been dramatically reduced for the past
three decades [29, 30]. The lateral feature size or linewidth
of a transistor has been shrunk by almost 50 times from
about 10 m to the 100 nm range, allowing over 10,000
times more transistors to be integrated on a single chip.
Microprocessors have evolved from their 0.1 MHz ancestors used for watches and calculators in the early 1970s to
the current 2 GHz engines for personal computers. Memories have grown from 1-Kb pioneers used almost exclusively
for mass storage in central computers to the 128/256-Mb
dynamic random access memory commonly used in personal
computers today. Most advanced chips on the market now
have feature sizes of 100 nm. According to the Semiconductor Industry Association’s International Technology Roadmap
for Semiconductors [31], the feature sizes for lithography
were projected as follows: 130 nm in 2001, 100 nm in 2003,
80 nm in 2005, 35 nm in 2007, 45 nm in 2010, 32 nm in
2013, and 22 nm in 2016. The wafer size has increased
from 2 inches in the early 1970s to the current 12 inches.
Therefore, the performance of ICs has been dramatically
improved, and the cost for manufacturing has been dramatically reduced. However, the device scaling is approaching its
limit. It was suggested that MOS device scaling might not be
extended to below 10 nm because of physical limits such as
power dissipation caused by leakage current through tunneling [32–34]. In addition, once electronic devices approach
the nano- and molecular scale, the bulk properties of solids
are replaced by the quantum-mechanic properties of a relatively few atoms such as energy quantization and tunneling.
It is therefore important to search for alternative devices for
Si MOS devices.
2.3. Quantum-Effect Devices
In order for a transistor-like device to operate on the nanoand molecular scale, it would be advantageous if it operated based on quantum mechanical effects. Even though
the study of single-electron charging effects with granular
metallic systems dates back to the 1950s [35, 36], it was the
research of Likharev in 1988 that laid much of the groundwork for understanding single-charge transport in nanoscale
tunnel junctions [37, 38]. When a small conductor (island) is
initially neutral, it does not generate any appreciable electric
field beyond its border. In this state, a weak external force
(due to electric field) may bring in an additional electron
from outside. The net charge in the island is (−e) and the
resulting electric field repulses the following electrons which
might be added. In order to have an electron to be added
it needs to overcome the charging energy and its kinetic
energy. Thus, the electron additional energy Ea is given by
E a = Ec + E k
Here Ec is the charging energy that is given by
Ec =
e2
C
where e is the charge of electron and C is the capacitance
of the conductive island. The kinetic energy is expressed as
Ek =
1
gF V
where gF is the density of states on the Fermi surface
and V is the volume of the island.
For the island diameter > 2 nm, Ec Ek . Thus
Ea ≈ Ec =
e2
2C
For the 100 nm-scale island, Ea is of the order of 1 meV,
corresponding to ∼10 K in temperature. If the island size is
reduced to below 10 nm, Ea approaches 100 meV, and some
single-electron effects become visible at room temperature.
Among quantum-effect devices, single-electron transistors
have been most extensively studied [38–40]. The basic structure of a SET is shown in Figure 3a. An island or quantum
dot is placed between two electrodes (source and drain) with
the third electrode (gate) is placed by its side. When a voltage is applied, an electron tunnels onto the island and the
charging energy is increased by Ea ≈ e2 /2C and this increase
acts as a barrier to the transfer of any further electrons. At
small source–drain voltage, there is no current. The I–V
characteristic is shown in Figure 3b. The current is blocked
from −Vc to Vc , called Coulomb blockade. When the source–
drain voltage is increased and reaches a level greater than
Vc , where the energy barrier is eliminated, electrons can
cross the island and the current increases with the applied
voltage. The threshold voltage Vc is a periodical function of
gate voltage.
Coulomb charging effects were originally observed in
metallic film by Gorter in 1951 [35]. The first successful
metallic single-electron transistor was made by Fulton and
Dolan in 1987 [36]. They used a relatively simple technique
in which two layers of aluminum were evaporated in-situ
from two angles through the same suspended mask formed
by direct e-beam writing. Since then, single-electron transistors have been demonstrated in numerous experiments using
a wide variety of device geometry, materials, and techniques.
SETs based on metallic nanodots were fabricated. Chen
et al. [41] reported that SETs with metal dots of 20–30 nm
and gaps of 20–30 nm were fabricated by ionized beam evaporation. The electrical results showed clear Coulomb blockade at temperature as high as 77 K. Novel lateral metallic
SETs can be based on gold colloidal particles. These particles are very uniform in size and can be obtained in a range
(a)
(b)
I
Gate
–V/2
Source
Proof's Only
V/2
Drain
–VC
VC
V
Island
Figure 3. (a) Schematic structure of a capacitively coupled singleelectron transistors and (b) its source–drain dc I–V curves.
922
4
of sizes. The devices can be fabricated by placing the particles in the gap between the source and drain. Klein et al.
[42] obtained the Coulomb blockade characteristics based
on gold colloidal particles at 77 K. Nakamura et al. [43] fabricated Al-based SETs, which operated at 100 K. Shirakashi
et al. [44] fabricated Nb/Nb oxide-based SETs at room temperature T = 298 K). The further reduction of the tunnel
junction is performed by scanning probe microscope (SPM)based anodic oxidation. The Coulomb blockade characteristics were clearly shown at room temperature.
Single-electron effects have also been observed in a number of semiconductor based structures. The first device
was realized by squeezing the two-dimensional electron gas
(2DEG) formed at the AlGaAs/GaAs heterostructure [45].
It consists of a pattern of metal gates evaporated onto
the semiconductor surface. The voltages were applied to
the gates to squeeze the 2DEG so that islands and tunnel
barriers were formed. Coulomb blockade can be observed
if the regions are sufficiently squeezed. Coulomb blockade effects have also been demonstrated on silicon based
devices. A number of experiments have been reported on
structures based on silicon-on-insulator (SOI). This is particularly important because silicon processing technology is
the mainstream technology in the semiconductor industry.
The silicon based SET technology can be easily integrated
into the mainstream technology once it is successful. Ali
and Ahmed [46] showed the first SOI-based SETs with clear
Coulomb blockade. Leobandung et al. [47] also demonstrated silicon quantum-dot transistors with a 40-nm dot.
The Coulomb blockade was clearly seen at temperature
of 100 K. Takahashi et al. [48] and Kurihara et al. [49]
scaled the silicon-based SETs to make significantly smaller
islands and obtained Coulomb oscillation at temperatures
approaching room temperature. Zhuang et al. [50] reported
fabrication of silicon quantum-dot transistors with a dot of
∼12 nm with a clear Coulomb blockade at 300 K. Guo
et al. [51] successfully fabricated a silicon single-electron
transistor memory, which operated at room temperature.
The memory is a floating gate MOS transistor in silicon with
a channel width (∼10 nm) smaller than the Debye screening length of a single electron and a nanoscale polysilicon
dot (7 nm × 7 nm) as the floating gate embedded between
the channel and the control gate. Storing one electron on
the floating gate screens the entire channel from the potential on the control gate and leads to a discrete shift in the
threshold voltage, a staircase relation between the charging
voltage and the shift. SETs based on Si nanowires have also
been demonstrated [52]. It was shown that quantum wires
with a large length to width ratio show clear Coulomb oscillations at temperatures up to 77 K.
3. SYNTHESIS AND ELECTRICAL
PROPERTIES OF CARBON
NANOTUBES
3.1. Synthesis of Carbon Nanotubes
Although this chapter focuses on nanoelectronic devices,
I still cover some of synthesis methods and approaches
which may be helpful for interested readers. It should be
Nanotubes for Nanoelectronics
pointed out that I am unable to include all the papers in
synthesis because extensive research has been conducted for
growth of carbon nanotubes.
Although multiwall carbon nanotubes were discovered in
1991 by Iijima, it is quite likely that such MWNTs were
produced as early as the 1970s during research on carbon
fibers [2]. The multiwall carbon nanotubes discovered in
1991 were obtained from the fullerene soot produced in an
arc discharge [1]. As early as in 1986, Saito of the University of Kentucky studied the soot produced by a candlelike methane flame. A quartz fiber was inserted into the
flame from the side and left there for a certain period of
time [53]. When the fiber was raised to a certain height, a
smooth film was coated on the fiber surface, which appeared
to be brown in color. With increase of the sampling height
beyond the critical height, the color of the deposited material changed from brown to black, and its surface appearance
also changed from smooth to a rough and bumpy structure. The SEM analysis identified the rough surface material to be soot and the initial light brown material from the
methane flame to be polyhedral-shaped crystal-like particles
[54]. The deposit from the acetylene flame had a spiderweb shape of entangled, long, narrow diameter strings, of
which the detailed structure remained unknown until recent
TEM study [55]. It was a surprise that the recent TEM study
showed that the entangled long strings synthesized in 1986
are carbon nanotubes, which were discovered later by Iijima
in 1991. Recently Saito’s group repeated his 1986 experiments and synthesized CNTs using methane flames [56]
and ethylene flames [57]. In 1993, Iijima and Ichihashi [11]
synthesized single-wall carbon nanotubes of 1-nm diameter.
Bethune and co-workers [12] also, at the same time, synthesized single-wall carbon nanotubes using cobalt catalyst. The
research on carbon nanotubes really took off when Smalley and co-workers at Rice University found a laser ablation
technique that could produce single-wall carbon nanotubes
at yields up to 80% instead of the few percent yields of early
experiments [58–60]. Kong and co-workers [61] at Stanford
University used a chemical vapor deposition (CVD) technique to grow carbon nanotubes by decomposing an organic
gas over a substrate covered with metal catalyst particles.
The CVD approach has the potential for making possible
large-scale production of nanotubes and growth of nanotubes at specific sites on patterned Si substrates [62, 63].
3.2. Electronic Structures
of Carbon Nanotubes
Just in one year after the discovery of carbon nanotubes,
their electronic structures were theoretically studied based
on local-density-functional calculation [8], tight-binding
band-structure calculation [9, 10, 64]. Figure 4a shows how
to construct a carbon nanotube by wrapping up a single
sheet of graphite such that two equivalent sites of the hexagonal lattice coincide; that is, point C coincides with the
origin (0, 0) [65]. The wrapping vector C, which defines
the relative location of the two sites, is specified by a pair
of integers n m that relate C to the two unit vectors
a1 and a2 (C = na1 + ma2 ). A tube is called “armchair”
if n equals m, and “zigzag” in the case m = 0. All other
tubes are of the “chiral” type with a finite wrapping angle
923
5
Nanotubes for Nanoelectronics
(c)
Tubule
Axis
axi
s
(d)
5
4
E (eV)
(a)
H
E (eV)
T φ
(A)
3
tub
e
2
zigzag
(11,0)
(0,0)
chir
al
φ
a2
(0,7)
M
Γ
arm
C
cha
(11,7)
ir
(B)
no. 10
Proof's Only
no. 11
no. 1
no. 7
no. 8
T
φ
H
1 nm
Figure 4. Relation between the hexagonal carbon lattice and the chirality of carbon nanotubes. (A) Construction of a carbon nanotube from
a single graphene sheet by rolling up the sheet along the wrapping vector C. (B) Atomically resolved STM images of individually single-wall
carbon nanotubes showing chirality. Reprinted with permission from
[65], J. W. G. Wildoer et al., Nature 391, 59 (1998). © 1998, Macmillan
Publishers Ltd.
(0 < < 30 ). Figure 4b shows the STM images of singlewall carbon nanotubes [65]. Tube 10 has a chiral angle =
7 and a diameter d = 13 nm, which corresponds to the
(11, 7) type of panel A. The dependence of the electronic
structure of nanotubes on the tube indices n m can be
understood by taking the two-dimensional graphene sheet as
a starting point. In the circumferential direction (along C),
the periodic boundary conditions C · k = 2q can be applied,
where k is the wave vector and q is an integer. This leads to
a set of allowed values for k, which can be substituted into
the dispersion relations for the tube, with q representing the
various modes. Electronic energy band structure calculations
[3, 8–10, 64] predicted that armchair n = m tubes behave
like metallic. For all other tubes (chiral and zigzag) there
exist two possibilities. If n − m/3 is an integer, tubes are
expected to be metallic, and if n − m/3 is not an integer,
tubes are predicted to be semiconducting with an energy
gap depending on the diameter. The energy gap can be
expressed as Egap = 20 aC−C /d, where 0 is the C–C tightbinding overlap energy, aC−C is the nearest neighbor C–C
distance (0.142 nm), and d is the diameter. Figure 5 shows
the calculated energy band structure of zigzag nanotubes
(12, 0) in (c) and (13, 0) in (d). [The geometric structure of
the tubes and the first Brillouin zone of a graphene sheet are
EF
0
–1
–1
–2
–2
–3
–3
–4
–4
–5
Γ
X
–5
Γ
X
Figure 5. (a) The geometric configuration for a single-wall carbon
nanotube n 0. (b) The first Brilluoin zone of a graphite sheet and
the wave vector allowed by the periodic boundary condition along the
circumference for n = 6 (solid lines). Band structures of (c) (12,0) and
(d) (13,0) single-wall nanotubes. Reprinted with permission from [9],
N. Hamada et al., Phys. Rev. Lett. 68, 1579 (1992). © 1992, American
Physical Society.
shown in (a) and (b).] The tube (12,0) is metallic, satisfying
the condition of n − m/3 being integer; and the tube (13,0)
is semiconducting with an energy gap of 0.697 eV, which falls
into the category of n − m/3 being noninteger. Figure 6
shows the calculated energy band gaps of tubes n 0 with
n = 6–15. For n = 6, 9, 12, 15 [i.e., n − m/3 is integer],
energy gaps are almost zero, and for n = 7 8 10 11 13 14,
[i.e. n − m/3 is noninteger], the energy gaps are ranging from 0.6 to 1.2 eV. Figure 7 shows the calculated onedimensional (1D) electronic density of states for (a) a (9,0)
nanotube and (b) a (10,0) nanotube [66]. The 1D density of state (DOS) of both nanotubes shows a series of
spikes. Each spike corresponds to the energy threshold for
an electronic subband caused by the quantum confinement
of electrons in the radial and circumferential directions of
nanotubes. The (9,0) nanotube is metallic and the (10,0)
tube is semiconducting.
Experimental measurements [65, 67] of the energy
bands of nanotubes confirmed these theoretical calculations.
Figure 8a shows a selection of I–V curves obtained by scanning tunneling spectroscopy (STS) on different tubes [65].
Most curves show a low conductance at low bias, followed
by several kinks at larger bias voltages. Figure 8b shows
1.5
band gap (eV)
a1
K
(b)
3
1
EF
0
θ
4
2
1
unit
5
1.0
0.5
0
6
12
9
15
n
Figure 6. The energy bandgap as a function of the number of hexagons
on the circumference for a single-wall nanotube n 0. Reprinted with
permission from [9], N. Hamada et al., Phys. Rev. Lett. 68, 1579 (1992).
© 1992, American Physical Society.
924
6
Nanotubes for Nanoelectronics
(a)
Proof's Only
(b)
Figure 7. Calculated one-dimensional electronic density of states for
(a) a (9,0) nanotube and (b) a (10,0) nanotube. Reprinted with permission from [66], M. S. Dresshaus, Nature 391, 19 (1998). © 1998,
Macmillan Publishers Ltd.
a
b
the dI/dV curves. There are two categories: the one has a
well-defined gap values around 0.5–0.6 eV and the other has
significantly larger gap values of ∼1.7–2.0 eV [65]. The gap
value of the first category agrees very well with the predicted
gap values for semiconducting tubes. As shown in Figure 9c,
the energy gap decreases as the tube diameter d increases.
This also agrees well with theoretical gap values obtained
for an overlap energy 0 = 27 ± 01 eV, which is close
to the value 0 = 25 eV suggested for a single graphene
sheet [3]. The very large bandgaps observed for the second category of tubes, 1.7–2.0 eV, are in good agreement
with the values of 1.6–1.9 eV obtained from one-dimensional
dispersion relations for a number of metallic tubes with
n − m/3 being integer [65]. These metallic nanotubes are
expected to have a small but finite DOS near the Fermi
energy (EF ) and the apparent “gap” is associated with DOS
peaks at the band edges of the next one-dimensional modes.
Sharp van Hove singularities in the DOS are predicted at
the onsets of the subsequent energy bands, reflecting the
one-dimensional character of carbon nanotubes (see Fig. 7).
The derivative spectra indeed show a number of peak structures (Fig. 8b). For semiconductors, it has been argued that
dI/dV /I/V represents the DOS better than the direct
derivative dI/dV, partly because the normalization accounts
for the voltage dependence of the tunnel barrier at high
bias [68, 69]. In Figure 9, dI/dV /I/V is shown, where
sharp peaks are observed, resembling that predicted for van
Hove singularities. The experimental peaks have a finite
height and are broadened because of hybridization of wave
functions. Raman scattering experiments also support the
one-dimensional subband of nanotubes [70, 71]. Resistivity measurements of armchair SWNTs also suggested their
metallic behavior, consistent with the theoretical calculation
[72, 73]. In addition, momentum-dependent high-resolution
electron energy-loss spectroscopy was performed on purified
SWNTs [74]. Two groups of excitations have been found.
–
c
–
Figure 8. (a) Current–voltage curves obtained by tunneling spectroscopy on various nanotubes. (b) The derivatives dI/dV show two
groups: a semiconducting one with gap values around 0.5–0.6 eV and a
metallic one with gap values around 1.7–1.9 eV. (c) Energy gap versus
diameter of semiconducting chiral tubes. Reprinted with permission
from [65], J. W. G. Wildoer et al., Nature 391, 59 (1998). © 1998,
Macmillan Publishers Ltd.
Figure 9. (dI/dV)/(I/V) which is a measure of the density of states versus
V for nanotube 9. The left inset displays the raw dI/dV data, and the
right inset is the calculated DOS. Reprinted with permission from [65],
J. W. G. Wildoer et al., Nature 391, 59 (1998). © 1998, Macmillan Publishers Ltd.
925
7
Nanotubes for Nanoelectronics
One group is nondispersive and the energy position is characteristic of the separation of the van Hove singularities in
the electronic DOS of the different types of nanotubes. The
other one shows considerable dispersion and is related to a
collective excitation of the -electron system [74].
As pointed out by Dresselhaus [66], these results [66, 67]
showed a wide range of helicities for SWNTs which contradict the narrow distribution of chiral angles determined by
Raman scattering experiments [71] carried out on SWNT
ropes synthesized by the same technique. In addition,
van Hove singularities (energy threshold for an electronic
subband) were also clearly resolved [65] in the experimental DOS of both chiral and achiral nanotubes. The observation of these well-separated and clearly resolved sharp
spikes in the DOS of SWNTs with chiral symmetry was not
expected [66]. Further calculation of the + electron
densities of states of chiral carbon nanotubes using a tightbinding Hamiltonian showed that the electronic structures
of SWNTs with chiral symmetry are similar to the zigzag and
armchair ones [73, 74]. Fluorescence has also been observed
directly across the bandgap of semiconducting carbon nanotubes, supporting the theoretical calculation of energy band
structure of carbon nanotubes [77]. Most SWNTs synthesized using the current technologies are ropes consisting
of many individual SWNTs. The first-principle calculation
of electronic band structure of close-packing of individual
nanotubes (10,10) into a rope showed that a broken symmetry of the (10,10) tube caused by interactions between
tubes in a rope induces a pseudogap of about 0.1 eV at the
Fermi level [78]. This pseudogap strongly modifies many of
the fundamental electronic properties of carbon nanotube
ropes. Structures of molecular electronic devices ultimately
depend on tuning the interactions between individual electronic states and controlling the detailed spatial structure of
the electronic wave functions in the constituent molecules.
It is amazing that the two-dimensional images of electronic
wave functions in metallic SWNTs have been obtained using
STS [79]. These measurements reveal spatial patterns that
can be directly understood from the electronic structure of a
single graphite sheet. This represents an elegant illustration
of Bloch’s theorem at the level of individual wave functions.
3.3. Quantum Transport
of Carbon Nanotubes
The electrical transport experiments on individual tubes
are highly preferred. The first measurements on individual
nanotubes were carried out on MWNTs [80–84]. Langer
et al. [82] reported on electrical resistance measurements
of an individual MWNT down to a temperature of T =
20 mK. The conductance exhibited a ln T dependence and
saturated at low temperature. A magnetic field applied perpendicular to the tube axis increased the conductance and
produced aperiodic fluctuations. Their data also support
two-dimensional weak localization and universal conductance fluctuations in mesoscopic conductors. These early
studies on MWNTs suggested defect scattering, diffusive
electron motion, and localization with a characteristic length
scale of only a few nanometers. In addition, the electrical
properties of individual MWNTs have been shown to vary
strongly from tube to tube.
3.3.1. Ballistic Transport
It came as a surprise when the first experiments on individual SWNTs showed that nanotubes could have delocalized wave functions and behave as true quantum wires
[85, 86]. Electrical measurement indicates that conduction
occurs through well separated, discrete electronic states that
are quantum-mechanically coherent over long distance, at
least >140 nm [86]. Theory predicts that the electrons flow
ballistically through carbon nanotubes and that the conductance is quantized [87–90]. Quantized conductance results
from the electronic waveguide properties of extremely fine
wires and constrictions. When the length of the nanotube
is less than the mean-free path of electrons, the electronic
transport is ballistic (i.e., each transverse waveguide mode or
conduction channel contributes G0 = 2e2 /h to the total conductance). Theoretical calculation indicates that conducting
single shell nanotubes have two modes or two conduction
channels [87–90]; this predicts that the conductance of a
single-walled nanotube is 2G0 independent of diameter and
length. Another important aspect of ballistic transport is that
no energy is dissipated in the conductor and the Joule heat is
dissipated at the contacts of metal and nanotubes. Conductance measurements on MWNTs revealed that only one conduction channel G0 exists in MWNTs, which conduct current
ballistically over a length of 4 micrometers [91]. Recently,
quantized conductance has been observed in SWNTs [92],
which has two conduction channels 2G0 , in agreement with
the theoretical calculation. Theoretical studies also suggests
that conduction electrons in armchair nanotubes experience
an effective disorder averaged over the tube’s circumference,
leading to electron-mean-free paths that increase with nanotube diameter [93]. This increase should result in exceptional ballistic transport properties and localization lengths
of 10 m. For (10,10) armchair nanotubes, the mean-free
path of 7.5 m is obtained [93].
The fundamental reason for ballistic transport of carbon
nanotubes is their perfect symmetric and periodic structure.
It was shown that defects introduced into the nanotubes
serve as scattering centers [94], which destroys the perfect structure. Theoretical calculation also showed that the
absence of backscattering was demonstrated for single impurity with long range potential in metallic tubes [95–97]
and a stepwise reduction of the conductance was inferred
from multiple scattering on a few lattice impurities [98, 99].
Therefore, chemically doped semiconducting SWNTs may
behave as diffusive conductors with shorter mean-free paths.
It has been reported experimentally that mean-free paths
of SWNTs are lower than the ones of reported structurally
equivalent metallic SWNTs [100]. The backscattering contribution to the conductivity has been demonstrated to be
more significant for doped semiconducting systems [101].
3.3.2. Other Transport Properties
Zeeman Effect Tans et al. [86, 102] observed an excited
state by applying a magnetic field perpendicular to the tube
axis, which moved relative to the ground state at a rate corresponding to a g-factor of 2.0 ± 0.5, consistent with the
expected free-electron Zeeman shift. Cobden et al. [103]
later studied the spin state by applying a magnetic field along
the tube axis of the nanotube rope. It is concluded that as
926
8
successive electrons are added, the ground state spin oscillates between S0 and S0 + 21 , where S0 is most likely zero.
This results in the even/odd nature of the Coulomb peaks,
which is also manifested in the asymmetry of the current–
voltage characteristics and the peak height [106]. It is suggested that the g-factor of the Zeeman split is 2.04 ± 0.05
[104].
Aharonov–Bohm Effect When electrons pass through a
cylindrical electrical conductor aligned in the magnetic field,
their wavelike nature manifests itself as a periodic oscillation
in the electrical resistance as a function of the enclosed magnetic flux. This phenomenon reflects the dependence of the
phase of the electron wave on the magnetic field known
as the Aharonov–Bohm effect [105], which causes a phase
difference, and hence interference, between partial waves
encircling the conductor in opposite directions. Theoretical studies showed [86, 106] that upon applying a magnetic
field along the tube axis, the electronic structure of a carbon
nanotube drastically changes from a metal to a semiconductor or from a semiconductor to a metal during variation of
magnetic flux . The energy dispersion without the spin-B
interaction is periodic in , with a period 0 , as a result
of the Aharonov–Bohm effect. Magnetoresistance measurements were carried out on individual MWNTs, which exhibit
pronounced resistance oscillations as a function of magnetic
flux [107]. The oscillations are in good agreement with theoretical predications for the Aharonov–Bohm effect in a
hollow conductor with a diameter equal to that of the outermost shell of the nanotubes. Significant electron–electron
correlation has been observed in experiments [108]. Electrons entering the nanotube in a low magnetic field are
observed to have all the same spin direction, indicating spin
polarization of the nanotube. When the number of electrons
is fixed, variation of an applied gate voltage can significantly
change the electronic spectrum of the nanotube and can
induce spin-flips [108].
Luttinger Liquid Electron transport in conductors is usually well described by Fermi-liquid theory, which assumes
that energy states of electrons near the Fermi level EF are
not qualitatively altered by Coulomb interactions. In onedimensional systems, however, even weak Coulomb interactions cause strong perturbations. The resulting system,
known as Luttinger liquid, is predicted to be distinctly different from its two- or three-dimensional counterpart [109].
Coulomb interactions have been studied theoretically for
SWNTs [110, 111] and MWNTs [112]. Long-range Coulomb
forces convert an isolated N N armchair carbon nanotube into a strong renormalized Luttinger liquid [110]. At
high temperatures, anomalous temperature dependence for
the interaction, resistivity due to impurities, and power-law
dependence for the local tunneling density of states were
found. At low temperatures, the nanotube exhibits spincharge separation, signaling a departure from orthodox theory of Coulomb blockade. Experimental measurements of
the conductance of bundles (“ropes”) of SWNTs as a function of temperature and voltage confirmed these theoretical
studies [113].
Nanotubes for Nanoelectronics
4. SINGLE-ELECTRON TRANSISTORS
4.1. Single-Wall Carbon Nanotubes
In 1997, Bockrath et al. [85] reported the first single-electron
transport of a single bundle containing 60 single-wall carbon
nanotubes (10,10) with a diameter of 1.4 nm at a temperature of 1.4 K. The device structure (Fig. 10, left inset) consists of a single nanotube rope and lithographically defined
Au electrodes. The device has four contacts and allows different segments of the nanotube to be measured. The device
was mounted on a standard chip carrier and contacts were
wire bonded. A dc bias (Vg was applied to the chip carrier base to which the sample was attached. This dc bias
can be used as gate voltage Vg to modify the charge density along the tube. Figure 10 shows the I–V characteristics of the nanotube section between contacts 2 and 3 as
a function of temperature T . The conductance is strongly
suppressed near V = 0 for T < 10 K. Figure 11A shows conductance G versus gate voltage Vg at T = 13 K. The conductance curve consists of a series of sharp peaks separated
by regions of very low conductance. The peak spacing varies
significantly. The height of peaks also varies widely with the
maximum peak reaching e2 /h, where h is the Planck constant. The peak amplitude decreases with T (Fig. 11B) while
the peak width increases with T (Fig. 11C). These phenomena can be understood based on Coulomb blockade effect
described in Section 2.3. In this device, transport occurs by
tunneling through the isolated segment of the rope. Tunneling on or off this segment is governed by the single-electron
addition. The period of the peaks in gate voltage, "Vg , is
determined by the energy for adding an additional electron
to the rope segment.
In the same year (1997), Tans and co-workers [86] at
Delft University of Technology built molecular devices using
a metallic (armchair) SWNT as a quantum wire. Figure 12
shows the structure of the device. An individual SWNT with
a diameter of ∼1 nm is lying across two Pt electrodes with a
separation of 140 nm. The third electrode located ∼450 nm
Proof's Only
Figure 10. The I–V characteristics at a series of different temperatures
for the rope segments between contacts 2 and 3. Left inset: AFM image
of the fabricated device where the bright regions are metallic contacts.
Right inset: Schematic energy-level diagram of the two 1D subbands
near one of the two Dirac points with the quantized energy levels indicated. Reprinted with permission from [85], M. Bockrath et al., Science
275, 1922 (1997). © 1997, American Association for the Advancement
of Science.
927
9
Nanotubes for Nanoelectronics
A
B
C
B
A
Current (nA)
0.5
C
1
0
–4
0
4
0.0
A
B
C
–0.5
–4
–2
0
2
4
Bias voltage (mV)
Figure 11. (A) Conductance G versus gate voltage Vg at T = 13 K for
the rope segments 2 and 3. (B) Temperature dependence of a peak.
(C) Width of the peak in (B) as a function of T . Reprinted with permission from [85], M. Bockrath et al., Science 275, 1922 (1997). © 1997,
American Association for the Advancement of Science.
away from the nanotube functions as a gate. Their original
idea is to build a single-electron transistor using a SWNT
as a quantum wire. The electrical measurement was carried
out at a low temperature of 5 mK. The typical current–
voltage characteristics at various gate voltages are shown in
Figure 13a. The coulomb charging effect is clearly observed.
Coulomb charging occurs when the charging energy Ec =
e2 /2C kT. At low temperature, the Coulomb blockade
effect can be observed. The two traces in Figure 13b were
taken under identical conditions and show an occasional
doubling of certain peaks. This bistability was regarded as
the result of switching offset charges that shift the potential
of the tube [86].
Chemical doping was used to achieve quantum dots
and junctions for single-electron transistors [114]. Electrical measurements of the potassium (K) doped nanotube
reveal single-electron charging at temperature up to 160 K
[114]. The quantum dot is formed by inhomogeneous doping
along the nanotube length [115–119]. The p–n–p junction
Proof's Only
Figure 12. AFM tapping-mode image of a single-wall carbon nanotube on top of a Si/SiO2 substrate with two 15-nm-thick Pt electrodes.
Reprinted with permission from [86], S. J. Tans et al., Nature 386, 474
(1997). © 1997, Macmillan Publishers Ltd.
Figure 13. (a) Current–voltage curves of the nanotube at a gate voltage
of 88.2 mV (trace A), 104.1 mV (trace B), and 120 mV (trace C). Inset:
more I–Vbias curves with Vgate ranging from 50 mV (bottom curve) to
136 mV (top curve). (b) Current versus gate voltages at Vbias = 30 V.
Reprinted with permission from [86], S. J. Tans et al., Nature 386, 474
(1997). © 1997, Macmillan Publishers Ltd.
was obtained by chemical doping. The transport measurements of the junction showed that a well defined and
highly reproducible on-tube single-electron transistor has
been achieved [115]. It has been found that strong bends
(“buckles”) within metallic carbon nanotubes [2] act as
nanometer-sized tunnel barriers for electron transport [116].
Single-electron transistors operating at room temperature
have been fabricated by inducing two buckles in series within
an individual metallic SWNT by manipulation with an AFM
[117, 118]. The island with a length of 25 nm has been
achieved and the resulting SET clearly showed the Coulomb
blockade effect at room temperature [118]. Room temperature SETs have also been fabricated from SWNTs using
V2 O5 nanowires as masks for selective chemical doping
[118]. Single-electron devices based on SWNTs with the lineshaped top gates [120], triple-barrier quantum dots [121],
suspended quantum dots [122], field-induced p-type quantum dots [123], and kink-induced quantum dots [124] were
fabricated. The microwave response of coupled quantum
dots in SWNTs has also been measured [125]. The Coulomb
oscillations for different microwave power were similar to
those for different bias voltages without microwave.
Collins and co-workers [126] investigated electrical transport by sliding the STM tip along a nanotube. Figure 14
shows the schematic procedure for measuring nanotube
characteristics using a single STM tip. From a position
of stable tunneling (Fig. 14A), the STM tip was initially
driven forward ∼100 nm into the nanotube film (Fig. 14B).
After retraction of the tip well beyond the normal tunneling range, nanotube material remained in electrical contact
with the tip (Fig. 14C). Conductivity measurements were
carried out by sliding the STM tip down along the nanotube while the tip remained electrically connected with the
nanotube (Fig. 14D). The continuous motion of the tip
allowed electrical characterization of different lengths of the
nanotube. This technique results in a position-dependent
electrical transport measurement along the extended lengths
of selected nanotubes. A series of I–V curves were recorded
928
10
Nanotubes for Nanoelectronics
A
B
Tunnel
Contact and adhesion
d = 1 nm
C
D
Retraction
Sliding contact
d = 20 nm
d = 2 µm
Figure 14. Schematic of the procedure for measuring nanotube characteristics with a single STM tip. Reprinted with permission from [126],
P. G. Collins et al., Science 278, 100 (1997). © 1997, American Association for the Advancement of Science.
at positions 1600, 1850, 1950, and 2000 nm as shown in
Figure 15. The first three curves are nonlinear but nearly
symmetric. At a position of 2000 nm the I–V characteristics abruptly changed to a marked rectifying behavior
(Fig. 15D). This response (Fig. 15D) was reproducible and
persistent for positions up to 2300 nm before the nanotube
was broken. It was suggested by Collins et al. [126] that the
position-dependent behavior gives strong evidence for the
existence of localized, well-defined, on-tube “nanodevices”
30
10
A
with response characteristics consistent with the theoretical predictions. The extreme changes in conductivity were
caused by contact with the localized nanotube defects that
greatly altered the local N E. Although the injected current predominantly indicates a graphitic behavior for the
nanotube rope, a nanotube defect at the contact point
would obscure and dominate the transport characteristics.
For example, the existence of a pentagon–heptagon defect
in the otherwise perfectly hexagonal nanotube wall fabric
can lead to sharp discontinuities in the electronic density
state along the tube axis. It is possible to have one portion of the nanotube with metallic characteristics almost
seamlessly joined to another portion that is semiconducting.
This “junction” constitutes a pure-carbon Schottky barrier.
The sliding STM probe indicates exactly this type of behavior as its position moves along the length of a nanotube by
only a few nanometers, indicating the existence of a localized nanotube nanodevice.
4.2. Multiwall Carbon Nanotubes
Although single-electron transistors were made first from
SWNTs [85, 86], a few reports [127–132] can be found for
fabrication of SETs using MWNTs. Roschier et al. [127]
of Helsinki University fabricated single-electron transistors
using MWNTs through manipulation by a SPM. Figure 16
shows the experimental procedure for rotating and moving a nanotube, and eventually the tube was set across the
electrodes with a gap of ∼300 nm. The electrical measurements of the device were done at low temperatures
B
20
5
10
0
0
Proof's Only
–10
–5
I (µA)
–20
–30
5
4
–10
0.3
C
D
0.2
3
2
0.1
1
0
0
–1
–0.1
–2
–3
–0.2
–4
–5
–1.0
–0.5
0
0.5
1.0
–0.3
–1.0
–0.5
0
0.5
1.0
V (V)
Figure 15. Different types of current–voltage characteristics, obtained
for contact points at different heights of (A) 1600, (B) 1850, (C) 1950,
and (D) 2000 nm along the carbon nanotube. Reprinted with permission from [126], P. G. Collins et al., Science 278, 100 (1997). © 1997,
American Association for the Advancement of Science.
Figure 16. AFM images during moving process. The 410 nm long
MWNT, the side gate, and the electrode structure are marked in the first
frame. The last frame represents the measured configuration, where
one end of the MWNT is well over the left electrode and the other end
is lightly touching the right electrode. Reprinted with permission [128],
L. Roschier et al., Appl. Phys. Lett. 75, 728 (1999). © 1999, American
Institute of Physics.
929
11
Nanotubes for Nanoelectronics
down to 4 K. The measured I–V curves display a 15 mV
wide zero current plateau across zero-voltage bias as shown
in Figure 17. The Coulomb blockade effect is clearly
observed below a few Kelvin and the nanotube behaves as
a SET. The asymmetry of the gate modulation, illustrated in
the inset for Vbias = 10 mV, indicates a substantial difference
in the resistance of the tunnel junctions. There is a clear
hysteresis in the I–Vbias curve at T = 120 mK. It is suggested
that this phenomenon can be attributed to charge trapping,
in which single electrons tunnel hysteretically across the concentric tubes. Roshier et al. [128] later constructed lownoise radio-frequency (rf) single-electron transistors using
MWNTs. Contact resistance between a metal and a nanotube is commonly on the order of quantum resistance
RQ = h/e2 = 266 k%. Hence, quantum fluctuations do not
destroy charge quantization and thus it is possible to construct sensitive electrometers based on electrostatically controlled single-electron tunneling. The rf-SETs are the best
electrometers at present [133]. As reported by Schoelkopf
et al. [133] of Yale University, the sensitivity
√ of rf-SETs
based on Al islands approaches 12 × 10−5 e/ Hz, near the
quantum limit at high frequencies. However, at frequencies
below 1 kHz, these devices are plagued by the presence of
1/f ' noise (' ∼1–2). The origin of 1/f ' noise is the trapping and detrapping of charges either in the vicinity of the
island or on the surface of the nanotube or in the tunnel barrier [134, 135]. One way to reduce the 1/f ' noise
in SETs is to avoid contact of the central island with any
dielectric material. In research by Roshier and co-workers
[128], a freestanding MWNT across two electrodes was used
as the island. The MWNT was moved onto the top of the
electrodes √
by an AFM tip. The 1/f ' noise of the SET is
6 × 10−6 e/ Hz at 45 Hz, close to the performance in the
best metallic SETs.
4.0
0.1
I (nA)
3.0
2.0
I (nA)
1.0
0
Proof's Only
–0.2
0.0
–1.0
0
Vgate (V)
0.2
The significance of the paper by Tans et al. [86] is not in
the quantum effect, but in the gate-induced modulation of
conductance of the metallic nanotube. Field-effect transistors were first demonstrated using a single semiconducting SWNT by Tans et al. [136], and using both a SWNT
and a MWNT by Avouris et al. [137–140]. Figure 18 shows
the structure of the carbon nanotube field-effect transistor (CNTFET) [137]. The two electrodes are separated by
300 nm and gate oxide (SiO2 ) is 140 nm. Figure 19 shows
output characteristics of a SWNT-FET consisting of a single SWNT with a diameter of 1.6 nm for several values
of the gate voltage. It is clearly seen that the source–drain
current is modulated by electric field. The field effect of
the MWNT-FET device was not observed [137]. The hole
mobility is estimated to be 20 cm2 /V s. In 1999, Dai and
co-workers [141] reported fabrication of FET using SWNTs
controllably grown on substrates. Figure 20 shows the I–V
curves at various gate voltages [141]. The asymmetry of
the I–V curves was regarded as being inherent to the
metal–tube–metal system. I–V curves after exchanging the
source and drain show nearly unchanged asymmetry. These
results suggest that the observed asymmetry is not caused
by asymmetrical parameters such as different contact resistance at the two metal–tube contacts [141]. It was suggested
that the asymmetry of I–V curves is due to high source–
drain bias [141]. The transconductance was estimated to be
0.1 mS/m.
5.1.1. Scaling of CNTFET
Theoretical studies [142] showed that the performance can
be significantly improved if the channel length and gate oxide
can be further scaled down. The I–V characteristics are similar to the ballistic Si MOSFETs except for the occurrence of
quantized channel conductance. Because of ballistic transport, the average carrier velocity reaches 27 × 107 cm/s
[145]. Theoretical studies [143] also show that the CNTFET can be scaled down to at least 5 nm. Because of the
ballistic transport, there is no energy dissipation except at
contacts, and terahertz operation may be possible. Recently
Wind and co-workers at IBM [144] improved their CNTFET
Au (source)
T = 22 K
T = 0.12 K
–3.0
–60
5.1. Field-Effect Transistors
MWNT or SWNT
T = 77 K
–2.0
5. FIELD-EFFECT TRANSISTORS, LOGIC
GATES, AND MEMORY DEVICES
Au (drain)
SiO2
–40
–20
0
20
40
60
Vbias (mV)
Figure 17. Measured I–Vbias curves at different temperatures when the
gate is at zero bias. The inset shows the gate modulation at Vbias =
10 mV (indicated by the arrow) at T = 120 mK. The enlargement in
the lower right corner shows the hysteretic behavior of the current.
Reprinted with permission from [128], L. Roschier et al., Appl. Phys.
Lett. 75, 728 (1999). © 1999, American Institute of Physics.
Si (back gate)
Figure 18. Schematic cross-section of the FET devices. A single nanotube of either multiwall or single-wall type bridges the gap between two
gold electrodes. The silicon substrate is used as back gate. Reprinted
with permission from [137], R. Martel et al., Appl. Phys. Lett. 73, 2447
(1998). © 1998, American Institute of Physics.
930
12
Nanotubes for Nanoelectronics
50
40
(a)
(a)
30
I (nA)
10
VG = 6 V
0
Proof's Only
I (µA)
20
–10
–20
–30
VG = –6 V
–40
–50
0
–100
–200
100
(b)
200
(b)
–7
VSD = 100 mV
I (nA)
40
G (S)
50
I (µA)
VSD (mV)
10
–8
10
–9
10
–10
10
–11
10
0
30
2
4
VG (V)
6
(c)
20
0
–4
I (µA)
10
–2
0
2
4
6
VG (V)
Figure 19. Output and transfer characteristics of a SWNT-FET: (a) I–
VSD curves measured for VG = −6, 0, 1, 2, 3, 4, 5, and 6 V. (b) I–VG
curves for VSD = 10–100 mV in steps of 10 mV. The inset shows that
the gate modulates the conductance by 5 orders of magnitude (VSD =
10 mV). Reprinted with permission from [137], R. Martel et al., Appl.
Phys. Lett. 73, 2447 (1998). © 1998, American Institute of Physics.
structure with top gate and very thin gate oxide (15 nm).
Figure 21 shows the device structure and its output characteristics. A single-wall carbon nanotube with a diameter of
1.4 nm was used as a semiconductor nanowire. The source
and drain were defined by e-beam lithography with a gate
length of 260 nm. I–V curves show excellent saturation and
on–off ratio of 105 . Table 1 shows a comparison of key device
performance parameters for a 260 nm gate length p-type
CNTFET with those of state-of-the-art Si MOS transistors,
a 15 nm gate Si p-type MOSFET [145] and a 50 nm gate
SOI p-type MOSFET [146]. It can be found that a CNTFET
has superior performance over Si MOSFETs. A CNTFET
exhibits a much higher ON current (Ion = 2100 A/m),
reasonable OFF current (Ioff = 150 nA/m), and very high
transconductance (2321 S/m). It should be noted that the
transconductance of the 15 nm gate Si p-MOSFET is only
975 S/m [145].
5.1.2. High Mobility
In [144], Wind et al. did not characterize the hole mobility
during transport. I will analyze the hole mobility as follows.
Because the I–V curves follow the classical transport model,
the transconductance in saturation is expressed as [147]
Gmsat =
p Cox W
VG − VT 2L
V
Figure 20. (a) Room-temperature I–V curves recorded with sample S1
for V in the range 3 to −3 V under various gate voltages. (b) I–V curves
recorded after exchanging the source–drain electrodes. (c) Symmetrical
I–V curves obtained by scanning V while biasing the two electrodes
at −V /2 and V /2, respectively. Reprinted with permission from [141],
H. Dai et al., J. Phys. Chem. B 103, 11246 (1999). © 1999, American
Chemical Society.
where p is the hole mobility. L and W are the gate length
and gate width separately. Cox is the gate oxide capacitance.
VG is the gate voltage and VT is threshold voltage (−0.5 V).
The gate width is considered to be half of the perimeter
of the CNT (diameter = 1.4 nm). Thus the mobility can be
calculated using
p =
Gmsat 2L
Cox W VG − VT Based on the given data of the transistor structure, the
hole mobility is 2018 cm2 V−1 s−1 . This is much larger than
the ideal hole mobility in bulk Si (∼400 cm2 V−1 s−1 ) and
200 × higher than the hole mobility (12 cm2 V−1 s−1 ) derived
from the 15 nm gate p-Si MOSFET [145]. These surprising
data indicate the potential of carbon nanotubes for high-speed
device application similar to III–V compound semiconductors
such as GaAs. It was reported that SWNTs are extremely
pure systems with large Fermi velocities of vF = 106 m/s and
ballistic transport over long distance [65, 91, 148]. Considering its unique 1D quantum wire electronic band structure
and ballistic transport over long distance, it is highly possible
for SWNTs to have extremely high mobility.
931
13
Nanotubes for Nanoelectronics
(a)
Gate Oxide
SiO2
Gate
(Al or Ti)
CNT
Drain (Ti)
Source (Ti)
Proof's Only
P–+Si
(b)
Figure 21. Schematic cross-section of top gate CNFET showing the
gate and source and drain electrodes. (b) Output characteristic of a top
gate p-type CNFET with a Ti gate and a gate oxide thickness of 15 nm.
The gate voltage values range from −0.1 to −1.1 V above the threshold
voltage, which is –0.5 V. Inset: Transfer characteristic of the CNFET for
Vds = −06 V. Reprinted with permission from [144], S. J. Wind et al.,
Appl. Phys. Lett. 80, 3817 (2002). © 2002, American Institute of Physics.
The high mobility of nanotube transistors estimated by
the present author has been confirmed by Rosenblat et
al. [149] and Kruger et al. [150]. Rosenblat et al. [149]
constructed a carbon nanotube transistor using an electrolyte as gate, which was inspired by the study of doping
effects using electrochemical gating [150, 151]. Figure 22
shows the device structure [149]. Catalyst islands containing
Fe(NO3 3 · 9H2 O, MoO2 (acac)2 , and alumina nanoparticles
were defined on SiO2 . Carbon nanotubes were then grown
by chemical vapor deposition. The source and drain with a
separation of 1–3 m (channel length) were defined using
Table 1. Comparison of key device performance parameters for a
260 nm gate length p-type CNTFET with those of state-of-the-art Si
MOS transistors: a 15 nm-gate p-type Si MOSFET and a 50 nm gate
p-type SOI MOSFET.
Types of transistors
Gate length (nm)
Gate oxide thickness (nm)
Threshold voltage (V)
ION (A/m) @
VDS = VGS − VT = 1 V
IOFF (nA/m)
Subthreshold slope (mV/dec)
Transconductance (S/m)
CNTFET Si MOSFET SOI MOSFET
[144]
[145]
[146]
260
15
−0.5
2100
150
130
2321
15
1.4
−0.1
265
∼500
∼100
975
50
1.5
−0.2
650
9
70
650
Source: Adapted with permission from [144], S. J. Wind et al., Appl. Phys. Lett.
80, 3817 (2002). © 2002, American Institute of Physics.
Figure 22. Optical micrograph of the device. Six catalyst pads (dark)
can be seen inside the area of the common electrode. Correspondingly, there are six source electrodes for electrical connection to tubes.
(b) AFM image of a tube between two electrodes. The tube diameter
is 1.9 nm. (c) Schematic of the electrolyte gate measurement. A water
gate voltage Vwg is applied to droplets through a silver wire. Reprinted
with permission from [149], S. Rosenblat et al., Nano Lett. 2, 869 (2002).
© 2002, American Chemical Society.
photolithography and a lift-off process. A micropipet is used
to place a small (∼10–20 m) saltwater droplet (NaCl solution) over the nanotube device. A voltage Vwg applied to a
silver wire in the pipet is used to establish the electrochemical potential in the electrolyte relative to the device. Then
the electrolyte functions as a liquid gate. The output characteristics of the electrolyte carbon nanotube FET are similar
to those in Figure 21. The transconductance of the transistor
reaches its maximum ∼20 S at a gate voltage of −0.8 V.
The mobility inferred from the conductance measurement is
in the range of 1000 to 4000 cm2 V−1 s−1 . The maximum onstate conductance is also shown for the same samples. Values on the order of e2 /h are routinely obtained, within a factor of 4 of the theoretical limit of 4e2 /h. Fuhrer et al. [152]
reported the hole mobility in a SWNT of 9000 cm2 V−1 s−1 ,
which is the highest value ever reported.
In addition, the field effect is clearly shown even at a
temperature of 5 K with a spikelike conductance, which is
attributed to the van Hove singularities [153]. AFM tips
were used to apply pointlike local gates to manipulate the
electrical properties of an individual SWNT contacted by
Ti electrodes [154]. The AFM tip contacting on a semiconducting SWNT causes depletion at a local point, leading
to orders of magnitude decrease of the nanotube conductance, while local gating to a metallic SWNT leads to no
change in conductance [154]. Theoretical study also suggests
that a quantum dot is formed because of the induced ntype together with the p-type near the metal contacts when
a positive gate voltage is applied on the p-type SWNT
[155]. The induced quantum dot enhances the conductance.
932
14
Because the energy bandgaps of semiconducting SWNTs
are inversely proportional to their diameter, large-diameter
SWNTs have smaller energy bandgaps. Transistors made of
large-diameter SWNTs exhibit ambipolar field-effect transistor behavior [156, 157]. Theoretical study showed that
the energy gap of a semiconducting nanotube can be narrowed, when the tube is placed in an electric field perpendicular to the tube axis (e.g., in the FET case) [158]. This
band-structure modulation may affect the electrical properties of CNTFETs. No experimental research has been
reported regarding this phenomenon. For characterization
of the semiconductor/oxide interface, capacitance–voltage
measurement is usually carried out on MOS capacitors. Theoretical study showed that the calculated C–V curves reflect
the local peaks of the 1D DOS in the nanotube [159]. This
might be used for diagnose the electronic structure of nanotubes, providing a more convenient approach than STM.
However, experimental measurement of the capacitance in
nanoscale is not easy because the accumulation capacitance
of a 1-m long nanotube MOS capacitor is only 1.5 × 10−4 pf
or 1.5 pf/cm [159].
Nanotubes for Nanoelectronics
A
Proof's Only
B
C
5.2. Logic Gates
In 2001, several groups [160–162] demonstrated logic circuits using carbon nanotube transistors. Bachtold et al. [160]
showed inverter, NOR gate, static random access memory (SRAM), and ring oscillator. Derycke et al. [161] and
Liu et al. [162] showed the CMOS inverter using both nand p-channel CNTFETs. Figure 23 shows individual device
structure and layout [160]. Unlike the previous nanotube
transistor structure using back gate, which applies the same
gate voltage to all transistors, the transistor structure consists of a microfabricated Al wire with native Al2 O3 as
gate insulator, which lies beneath a semiconducting nanotube that is electrically contacted to two Au electrodes. The
channel length is about 100 nm and gate oxide thickness
is about a few nanometers. This layout allows the integration of multiple nanotube FETs. The transistor is a p-type
enhancement mode FET with transconductance of 0.3 S
and on–off ratio of at least 105 . The transistor can operate at an ON current of 100 nA and an OFF current of
1 pA. The basic logic elements such as inverter, NOR gate,
SRAM, and ring oscillator were constructed as shown in
Figure 24. The inverter exhibits very good transfer characteristics. When input voltage is −1.5 V (logic 1), the output
voltage is 0 V (logic 0). When the input voltage is switched
to 0 (logic 0), the output becomes −1.5 (logic 1). Although
the transition is not as sharp as a Si MOSFET, it is still competitive. Because this inverter is constructed using a single
transistor, the standby current is still high. The ring oscillator
shows good oscillation waveforms although the oscillation
frequency is low in this pioneer stage. The inverters have
been constructed using complementary nanotube FETs similar to Si CMOS structure (complementary MOS), leading to
minimum standby power consumption [161, 162]. Figure 25
shows the CMOS inverter based on both n- and p-CNTFETs
and its transfer characteristic [161]. A single nanotube bundle is positioned over the gold electrodes to produce two
p-type CNTFETs in series. The device is covered by PMMA
and a window is opened by e-beam lithography to expose
part of the nanotube. Potassium is then evaporated through
Figure 23. Device layout. (A) Height image of a single-nanotube transistor, acquired with an atomic force microscope. (B) Schematic side
view of the device. (C) Height-mode atomic force microscope image
of two nanotube transistors connected by a Au interconnect wire. The
arrows indicate the position of the transistors. Reprinted with permission from [160], A. Bachtold et al., Science 294, 1317 (2001). © 2001,
American Association for the Advancement of Science.
this window to produce an n-CNTFET, while the other
CNTFET remains p-type. The transfer characteristics show
much better transition region (more steep slope).
5.3. Memory Devices
A concept for molecular electronics exploiting carbon nanotubes as both molecular device elements and molecular
wires for reading and writing information has been proposed
[163]. Each device is based on suspended, crossed nanotube geometry that leads to bistable, electrostatically switchable ON/OFF states. The device elements are naturally
addressable in large arrays by the carbon nanotube molecular wires making up the devices. These reversible, bistable
device elements could be used to construct nonvolatile random access memory and logic function tables at an integration level approaching 1012 elements per cm2 , and an
element operation frequency in excess of 100 GHz [163].
However, strictly speaking, these memory devices or logic
gates are not made of CNTFETs. Several groups [152, 164–
166] reported fabrication of memory devices using nanotube field-effect transistors. Air-stable n-type, ambipolar
CNTFETs were fabricated and used in nanoscale memory
cells [164]. The n-type transistors are achieved by annealing
nanotubes in hydrogen gas and contacting them by cobalt
electrodes. Due to their nanoscale capacitance, CNTFETs
933
15
Nanotubes for Nanoelectronics
Proof's Only
Figure 24. Demonstration of one-, two-, and three-transistor logic circuits with carbon nanotube FETs. (A) Output voltage as a function
of the input voltage of a nanotube inverter. Inset: Schematic of the
electronic circuit. The resistance is 100 M%. (B) Output voltage of
a nanotube NOR for the four possible input states (1,1), (1,0), (0,1),
and (0,0). The resistance is 50 M%. (C) Output voltage of a flip–flop
memory cell (SRAM) composed of two nanotube FETs. The two resistances are 100 M% and 2 G%. (D) Output voltage as a function of
time for a nanotube ring oscillator. The three resistances are 100 M%,
100 M%, and 2 G%. Reprinted with permission from [160], A. Bachtold
et al., Science 294, 1317 (2001). © 2001, American Association for the
Advancement of Science.
are extremely sensitive to the presence of individual charges
around the channel, which can be used for data storage
that operate at the few-electron level [165]. Figure 26 shows
the threshold voltage shift due to storage of charges (a,b,c),
device structure (d), and the voltage signal (Vout ) due to
charge storage [164]. In addition, the data-storage stability
of over 12 days has been achieved [165].
6. DOPING, JUNCTIONS,
AND METAL–NANOTUBE CONTACTS
A key technology advancement for the success of semiconductor industry is achievement of n- and p-type doping, junctions, and Ohmic contacts between metal and
Figure 25. (a) AFM image showing an intramolecular logic gate.
(b) Characteristics of the resulting intramolecular voltage inverter. The
thin straight line corresponds to an output/input gain of one. Reprinted
with permission from [161], V. Derycke et al., Nano Lett. 1, 453 (2001).
© 2001, American Chemical Society.
Figure 26. (a)–(c) High vacuum I–Vg data at Vds = 05 mV. Device
hysteresis increases steadily with increasing Vg due to avalanche charge
injection into bulk oxide traps. (d) Diagram of avalanche injection of
electrons into bulk oxide traps from the CNFET channel. (e) Data from
CNFET-based nonvolatile molecular memory cell. A series of bits is
written into the cell (see text) and the cell contents are continuously
monitored as a voltage signal (Vout ) in the circuit shown in the inset.
Reprinted with permission from [164], M. Radosavljevic et al., Nano
Lett. 2, 761 (2002). © 2002, American Chemical Society.
semiconductor. It is critical to achieve doping, pn junctions,
and Ohmic contacts for carbon nanotubes so that nanotube
electronics may evolve into a large industry.
6.1. Chemical Doping
Antonov and Johnson [167] observed current rectification
in a molecular diode consisting of a semiconducting SWNT
and an impurity. It was suggested that rectification resulted
from the local effect of the impurity on the tube’s band
structure. It is not clear what type of impurity it was. Lee
et al. [168] reported doping of SWNTs by vapor-phase reactions with bromine and potassium. Doping decreases the
resistivity of SWNTs at 300 K by up to a factor of 30
and enlarges the region where the temperature coefficient
of resistance is positive, which is the signature of metallic behavior. It was reported [169, 170] that potassium (K)
doping of SWNTs creates n-type carrier (electrons). The
doping effects were studied using the transistor structure.
The SWNT ropes were placed on top of Au electrodes
that have 500 nm separation. The electrodes were fabricated on the oxidized n+ -Si substrate which serves as gate.
The Au electrodes serve as source and drain. Figure 27
shows conductance vs gate voltage for an undoped nanotube rope (open circles) and an nanotube doped with potassium (solid circle) [169]. For the undoped nanotube, the
conductance increases with decreasing gate voltage, indicating p-type behavior. For the K-doped nanotube, the conductance increases with increasing gate voltage, indicating
n-type behavior. The typical values for the carrier density
are found to be ∼100–1000 electrons/m and the effective
mobility of electrons is eff ∼ 20–60 in early time [169].
Derycke et al. [171] reported two methods for conversion
of SWNTs from p-type to n-type. The first method involves
conventional doping with an electron donor and the second
934
16
Nanotubes for Nanoelectronics
Proof's Only
Figure 27. The conductance decreases with increasing gate voltage for
an undoped sample (open circles), indicating p-type behavior. Left
inset shows the energy band corresponding to this case. The conductance increases with increasing gate voltage after potassium doping at
a high doping level (solid squares) and at a low doping level (solid circles). Right inset shows the energy band corresponding to this situation.
Reprinted with permission from [169], M. Bockrath et al., Phys. Rev. B
61, R10606 (2000). © 2000, American Physical Society.
consists of annealing the metal nanotube contacts in vacuum to remove adsorbed oxygen. It has been found that
the main effect of oxygen adsorption is not to dope the
bulk of the nanotube, but to modify the Schottky barriers at
the metal–semiconductor contacts [172, 173]. It also found
that boron-doped MWNTs showed an enhanced room temperature conductivity [174]. However, theoretical calculation
showed that H2 O adsorption on a SWNT reduces conductance [175].
Figure 28. An SWNT with modulated chemical doping. (A) Device
scheme with the SWNT contacted by two Ni/Au electrodes. The right
half of the SWNT is doped by evaporating K atoms (black dots) from
an alkaline metal at 10−6 Torr. (B) Atomic force microscopy image of
the SWNT recorded before PMMA coating of the left half and doping.
The bright regions at the two ends are the electrodes. Dashed lines are
drawn to highlight the later PMMA-covered region. (C) A band diagram for the system. Reprinted with permission from [176], C. Zhou
et al., Science 290, 1552 (2000). © 2000, American Association for the
Advancement of Science.
6.2. Junctions and Metal–Nanotube
Contacts
Zhou et al. [176] published the first attempt for controllable chemical doping of individual carbon nanotubes to
achieve pn junctions. Figure 28 shows the device structure
for potassium doping and the resulting energy band structure [176]. The SWNT used in the doping experiments has
a diameter of ∼2 nm and a length of 3.5 m and is placed
across two metal electrodes. A back gate is used to modulate the carrier concentration by applying voltage on the
gate. A polymethylmethacrylate (PMMA) layer of 340 nm
thickness covers the left half of the nanotube, leaving the
right half exposed. Prior to doping, SWNT is a p-type
semiconductor. Potassium doping of the SWNT is carried
out in vacuum by electrical heating of a potassium source.
Figure 29A shows the I–Vg curves [176]. When Vg < −1 V
(Regime I), hole accumulation is achieved in the SWNT,
leading to p+ in the PMMA protected area due to increase
in hole concentration and n in the exposed region due to
compensation of electrons. In Regime II, electron concentration begins to increase, resulting in p+ n+ junction. I–V
curves of p+ n and p+ n+ junctions are shown in Figure 29B
and C. In the forward bias regime, a nice pn junction diode
is demonstrated. However, the reverse bias breakdown voltage is too small to be qualified as a diode [176]. Anyway,
this is the first result showing some possibility for fabrication
of nanotube-based pn junction diodes.
Figure 29. Electrical properties of the modulation-doped SWNT at
room temperature. (A) Current versus gate-voltage I–Vg curve
recorded under a bias voltage V = 1 mV. The drawings show the band
diagrams in four regimes. (B) and (C) I–V curves recorded in Regimes
I and II. The star and triangle in (A) marks the gate voltages for the I–
V curves in (B) and (C), respectively. Reprinted with permission from
[176], C. Zhou et al., Science 290, 1552 (2000). © 2000, American Association for the Advancement of Science.
935
17
Nanotubes for Nanoelectronics
Based on theoretical calculation, Chico et al. [177] proposed metal/semiconductor or semiconductor/semiconductor junctions, made of SWNTs, and based on the introduction
of topological defects in nanotubes. By introducing a pentagon and a heptagon into the hexagonal carbon lattice,
two tube segments with different electronic structures can
be seamlessly fused together to create semiconductor–
semiconductor or metal–semiconductor junctions [172, 178,
179]. Two carbon nanotubes have also been fused together
by high electric field [180]. The CNx /nanotube junctions
have been synthesized by a microwave plasma assisted CVD
method [181]. It is of particular interest that two SWNTs
were crossed over each other to form junctions [182]. Theoretical study also suggests that negative differential resistance may be observed in metal–nanotube–metal structures
[183]. Figure 30 shows the AFM image of a nanotube junction with a sharp kink of about 40 [172]. The kink consists of
five to seven defects. Figure 31 shows the I–V characteristics
of the kink metal–semiconductor junction [172]. The rectification effect is clearly seen in the figure. A model has
been proposed for the kink-shaped carbon nanotube Schottky diode, where the gate voltage modulation is included
[184, 185]. It has been observed that the nanotube Schottky diodes [172, 179] and the nanotube pn junctions [176]
exhibit much lower reverse-bias breakdown voltage than
conventional, micrometer-size Schottky diodes and pn junctions. A theoretical model has been proposed to describe
the potential barrier shape in ultrasmall Schottky diodes
[186]. It is suggested that for diodes smaller than a characteristic length lc (e.g., 80 nm for Nd = 1017 cm−3 ), Schottky barrier thickness becomes a function of the diode size.
Consequently, the contribution of tunneling to the total conductance is dramatically enhanced, resulting in lower reverse
breakdown voltage in nanoscale diodes [186]. The carbon
nanotube “T” junction with heptagons or pentagons for
joints has been proposed theoretically [187]. However, experimentally no “T” junction has been observed. Instead, “Y”
junctions have been produced through an anodic aluminum
oxide (AAO) template [188, 189] and directly on substrates
[190–196]. Theoretical calculation confirms the rectification
Proof's Only
Figure 30. Tapping-mode atomic force microscope amplitude images
of examples of nanotube junction devices. (a) and (b) Nanotubes that
contain a single kink of 36 and 41 respectively. (c) Illustration of
the carbon-bond network of a kink junction constructed between an
“armchair” tube and a “zigzag” tube, where 5 denotes a pentagon, 7
denotes a heptagon, and the atoms in the pentagon and heptagon are
highlighted by dark balls. Reprinted with permission from [172], Z. Yao
et al., Nature 402, 273 (1999). © 1999, Macmillan Publishers Ltd.
a
b
Figure 31. Current–voltage characteristics across the metal–
semiconductor junction of (a), showing rectifying behavior. The data
are taken at 100 K. The results at room temperature are similar, but
the data are noisier. Inset in (a): the I–V curve for the upper straight
segment measured at room temperature. In (a), the gate is grounded.
In (b): the gate voltages from right to left are 2, 1, 0, −1, −2, and
−4 V respectively. Inset in (b): expanded view of the small-current
region which shows more clearly the onset of conduction for both bias
polarities. Reprinted with permission from [172], Z. Yao et al., Nature
402, 273 (1999). © 1999, Macmillan Publishers Ltd.
effect of “Y” junctions [197–199]. When the positively biased
metal–nanotube contact (source electrode) is locally gated
with a negative gate voltage, a dramatic increase in transport current occurs because the Schottky barrier thickness
is reduced due to accumulation of holes near the contact
[200]. For the negatively biased metal–nanotube contacts, the
gate voltage has no effect on transport because no Schottky
barrier exists there [200]. Therefore, by positioning the gate
locally near one of the contacts, the nanotube FET is converted into a rectifying diode [200].
Zhang et al. [201] fabricated the first real Ohmic contacts between SWNTs and Ti by solid solid reaction: C
(nanotubes) + M (solid) → MC (solid), where M is metal.
The reaction was performed at a temperature ranging from
800 to 1000 C in ultrahigh vacuum or an inert atmosphere
to avoid volatile reactant [201]. The continuous transformation of the SWNT to carbide is controlled by the diffusion of
936
18
M to the C/M interface. The I–V curves showed a straight
line when the bias voltage is swept from −1 to 1 V, indicating a true Ohmic contact [201]. The resistance at the contact
is ∼0.3 k% [201], much better than the contact resistance
(∼20 k%) for the direct metal/nanotube contacts [202, 203].
7. NANOTUBE-BASED
NANOFABRICATION
Carbon nanotubes exhibit Coulomb-blockade effects, ballistic transport, and field effects. Of particular importance is
the field effect that may lead to the carbon nanotube electronics era. However, a critical issue for successful realization of carbon nanotube electronics is how to manipulate
the nanotubes so that large-scale manufacturing is possible.
7.1. Manipulation of Nanotubes
Using AFM and STM
Since discovery of carbon nanotubes [1], for electronic
device research, the majority of research has been focused
on manipulation of carbon nanotubes using the STM or
AFM [86, 118, 127, 163, 203–223]. Tans et al. [86] deposited
SWNTs on the SiO2 /Si substrate which had patterned metal
electrodes. An individual nanotube wire was put across
the Pt electrodes, which was imaged by an AFM. Physical
manipulation of nanotubes with the AFM tip, like rolling,
sliding, bending, and buckling, has been used to investigate
mechanical properties of nanotubes [211, 212]. Roschier
et al. [127] positioned a semiconducting multiwalled nanotube between two gold electrodes at the SiO2 surface. The
410 nm long MWNT was manipulated and positioned on
the gold electrodes by the AFM tip. Soh et al. [203] synthesized SWNTs on the patterned catalytic islands, which
are contacted with metal pads. Lefebvre et al. [204] developed a method to assemble SWNT circuits using a tapping mode AFM. Nanotubes can be controllably translated,
rotated, cut, and placed on top of one another by varying
the tip–sample force and the tip speed. These operations
can construct complex nanotube circuits. Of particular interest is that the suspended SWNT can be deformed locally
by the AFM tip, leading to a decrease in conductance
of the nanotube by two orders of magnitude [217–219].
This effect can be used to construct nanoelectromechanical
devices. Tight-binding simulation showed that this effect is
caused by the formation sp3 bonds because of the mechanical pushing action of the tip [217, 218]. Collins et al. at
IBM [205] demonstrated a simple method for permanently
modifying MWNTs by using current-induced breakdown to
eliminate individual shells one at a time. Carbon nanotubes can withstand remarkable current densities, exceeding
109 A/cm2 , because of their strong carbon–carbon bonding.
However, at high enough current nanotubes ultimately fail.
In MWNTs, this failure occurs in air at a certain threshold
power through the rapid oxidation of the outermost carbon shell. The mechanism for the breakdown initiation is
the current-induced defect formation. By using the electrical
breakdown technique, they can remove the MWNT shells
one by one. This controlled breakdown technique is also
performed with the help of STM or AFM. Study of the reliability and current carrying capacity showed that under high
Nanotubes for Nanoelectronics
current density (>109 A/cm2 ) no observable failure in the
nanotube structure and no measureable change in the resistance are detected at temperatures up to 250 C and for
time scales up to 2 weeks [224]. Although these processes and
techniques are especially useful for study of nanotubes’ physical
properties, they may not be appropriate for large-scale fabrication of nanotube-based devices and circuits with high yield.
7.2. Controllable Growth and Placement
of Nanotubes
Before we can think about building sophisticated nanotubebased circuitry, we must find how to grow the nanotubes in
specific locations, orientations, shapes, and sizes, as well as
how to construct nanotube devices at specific locations and
how to connect nanotube devices with each other.
7.2.1. Vertically Aligned
Carbon Nanotubes
Li et al. [225, 226] reported the first large-scale synthesis of vertically aligned carbon nanotubes by using CVD
catalyzed by iron nanoparticles embedded in mesoporous
silca. Vertically aligned arrays of isolated tubes with spacing between the tubes of about 100 nm were controllable
through the pores. This method has been extended to grow
freestanding carbon nanotubes on glass substrates at lower
temperature (<700 C) using nickel film as catalysts by
CVD [227–229] and also on Si substrates [231]. Because the
mesoporous structure of silica was not uniform, the controllability of tubes was not very good. It is well known
that the porous structure of AAO film exhibits hexagonal
close-packed nanopores with large-scale periodicity and high
densities [232–234]. Highly ordered and vertically aligned
carbon nanotube arrays was obtained when growth of nanotubes was carried out on AAO porous structure with cobalt
particles deposited into the bottom of the pores [235–
241]. Figure 32 shows the procedure for fabrication and
growth and the scanning electron microscope (SEM) image
of arrays of nanotubes [236]. It should be noted that these
highly ordered CNT arrays were successfully fabricated on
aluminum substrates. In order to incorporate the carbon
nanotubes into the Si electronics, growth of aligned nanotubes on Si substrates is imperative. AAO films were cracked
at about 300–400 C, whereas AAO on Nb was not damaged
at 1100 C in He gas because the thermal expansion coefficient of Nb is close to that of AAO. It is suggested that
the Nb layer under AAO may afford the durability for the
high temperature process [242]. CNTs were grown on the
AAO film based on 100-nm Nb film [242]. Unfortunately,
the as-grown nanotubes were not uniformly controllable and
sparse nanotubes were grown [242]. Hu et al. at the University of Kentucky [243, 244] successfully fabricated highly
ordered CNT arrays on silicon substrate using AAO template by the flame synthesis technique (see Fig. 33). In the
process, the Al film was not completely consumed during
anodization and the Al film that remained between the AAO
and Si substrate served as a buffer layer, resulting in smooth
surface without cracks after the high temperature process.
This demonstrated the feasibility for integration of carbon
nanotube devices with Si integrated circuits.
937
19
Nanotubes for Nanoelectronics
(a)
Aluminum
NCA template
Cobalt catalyst
Al anodization
Carbon nanotubes
Co deposition
C2H2 pyrolysis
(b)
200 nm
Figure 32. Schematic of fabrication process. (b) SEM image of the
resulting hexagonally ordered array of carbon nanotubes fabricated
using method in (a). Reprinted with permission from [236], J. Li et al.,
Appl. Phys. Lett. 75, 367 (1999). © 1999, American Institute of Physics.
7.2.2. Horizontally Aligned
Carbon Nanotubes
The first horizontally aligned growth of carbon nanotubes
was successfully carried out by Kroto’s group at the University of Sussex, UK, and Cheetham’ group at the University
of California at Santa Barbara, USA [245]. The cobalt film
deposited on a silica substrate was etched into tracks 1–
20 m wide using a laser beam. Laser beam generates tracks
free of cobalt, leaving cobalt particles evenly positioned
along the edges of the tracks. Carbon nanotube growth
was carried out using pyrolysis of 2-amino-4,6-dichloro-striazine. After growth, dense nanotubes were found lying
inside tracks and aligned from one edge to the other edge
of a track [245]. This is the first synthesis of horizontally
aligned nanotubes. Dai et al. [63, 141, 203, 246–253] continued extensive research on controllable growth of horizontally aligned carbon nanotubes on patterned Si substrates.
A network of suspended SWNTs was grown from Si towers
[249]. These suspended SWNTs might be used for interconnect of nanodevices. In order to enhance the directionality of growth, the electric field is introduced horizontally,
resulting in better aligned growth of SWNTs as shown in
Figure 34 [252]. This was also inspired by the field-assisted
growth of vertically aligned CNTs [254]. It was suggested
that the self-directed growth between the neighboring pillars
is due to the swing of the nanotube cantilever which contacts a catalyst particle in liquid phase as the nanotube grows
[255]. These results confirm the possibility of self-assembled
wiring of nanostructures. MWNTs were grown from the
cleaved side of a Si/SiO2 /Si mulitlayer structure to control
the diameter of nanotubes [256]. In order for large-scale
fabrication of nanodevices using CNTs, alternative selective
placement of CNTs other than an AFM or STM is desirable. Controlled placement of SWNTs on prepatterned Si
substrates has been achieved by a combination of the highly
selective adsorption of SWNTs onto open regions of aminofunctionalized SiO2 in a polymer resist, followed by liftoff [257]. Controlled placement has also been achieved by
electrical field-assisted alignment of CNTs under ac electric
field [258]. Of particular interest is the utilization of nanotubes for nanolithography. One example is to use nanotubes
as AFM tips to write nanopatterns [259]. Figure 35 shows
the AFM image of a 10 nm wide line (SiO2 fabricated
by a nanotube tip [259]. Nanoelectrodes with a spacing of
(a)
20 VDC, 0.5 V/µm
(b)
20 VDC, 0.5 V/µm
10 µm
(c)
10 µm
50 VDC, 0.5 V/µm
Proof's Only
10 nm
(a)
(b)
Figure 33. (a) Cross-sectional SEM images of CNT arrays (about
500 nm long) on Si substrate fabricated in our laboratories. (b) TEM
image of a CNT grown from the Al2 O3 template showing multiwalls.
Adapted with permission from [243], W. C. Hu et al., J. Nanosci. Nanotechnol. 2, 203 (2002). © 2002, American Scientific Publishers.
10 µm
Figure 34. SEM images of suspended SWNTs grown in various electric
fields. The spacing between the outer poly-Si electrodes is 40 m in
(a) and (b), and 100 m in (c). Reprinted with permission from [252],
Y. Zhang et al., Appl. Phys. Lett. 79, 3155 (2001). © 2001, American
Institute of Physics.
938
20
Nanotubes for Nanoelectronics
(b)
(a)
NANOTUBE
NANOPENCIL
NANOTUBE
NANOPENCIL
1 µm
1 µm
Figure 35. (a) AFM image of 2 nm tall, 10 mm wide, and 100 nm spaced
silicon-oxide (light) lines fabricated by a nanotube tip. Bias voltage =
−9 V; speed = 10 m/s; cantilever amplitude during lithography =
055 nm; cantilever amplitude = 96 nm. (b) Silicon oxide “words” written by the nanotube tip. Reprinted with permission from [259], H. Dai
et al., Appl. Phys. Lett. 73, 1508 (1998). © 1998, American Institute of
Physics.
∼30 nm have been demonstrated using a carbon nanotube
as a shadow mask, where a nanotube was suspended on
PR supporters [260]. Figure 36 shows the schematic of the
approach and Figure 37 shows the AFM image of the gold
electrodes with a gap of ∼30 nm [260]. Carbon nanotubes
have also been used as masks for plasma etching where a
∼20 nm nanowire beneath the nanotube was formed after
etching [261].
(a)
W
H
t
r
e
(b)
Carbo
n Nan
R2
R1
Proof's Only
otube
Metal
Substr
ate
Figure 36. (a) In a shadow mask method, the shadow or gap size ()
depends only on geometrical factors: the mask width or tube diameter t, the tube–substrate distance r, the evaporation source distance
H, and width W . (b) Carbon nanotubes are incorporated between
two layers of e-beam resist (R1 and R2) to act as a shadow mask preventing metal deposition at one point along a thin wire. The figure
illustrates the process after metal deposition. Reprinted with permission
from [260], J. Lefebvre et al., Appl. Phys. Lett. 76, 3828 (2000). © 2000,
American Institute of Physics.
Figure 37. AFM image of a sub-30 nm gap in a 350 nm wide gold wire
fabricated using a SWNT bundle. Individual SWNTs or small SWNT
bundles (dark gray lines in the image) have been contacted using this
method. Reprinted with permission from [260], J. Lefebvre et al., Appl.
Phys. Lett. 76, 3828 (2000). © 2000, American Institute of Physics.
8. SUMMARY
Carbon nanotube-based nanoelectronics have been reviewed
extensively, including electronic structure and transport
properties of carbon nanotubes, various electronic devices,
and nanotube-based nanofabrication. Since the discovery
of CNTs for more than 10 years, great progress has been
made in this field. Theoretical calculation predicted the
one-dimensional energy band structure of single-wall carbon
nanotubes with ballistic transport up to a few micrometers.
Experiments successfully confirmed the theoretical predication. There have been demonstrations of the basic functions
of carbon nanotube-based nanoelectronic devices such as
single-electron transistors, field-effect transistors, logic gates,
and memory devices. There is an almost limitless number
of new geometries and topics waiting to be explored and
all kinds of new structures to be created [262]. Upon comparison of their performance, carbon nanotube field-effect
transistors are superior over Si MOS transistors. It is very
promising to use carbon nanotube field-effect transistors as
building blocks for large-scale integrated circuits when the
current silicon technology reaches the end of its roadmap.
However, incorporation of the CNT devices to the existing Si manufacturing process is still far away. The current
practice of fabrication of CNT transistors relies on arduous
contacting of randomly distributed CNTs from suspension
or time-consuming manipulation by AFM. Although great
progress has been made in controllable growth and placement of carbon nanotubes, a planar process with high yield,
which is the cornerstone of silicon technology, has not yet
been achieved in the carbon nanotube process [263]. It is
believed that in the next 10 to 20 years progress in process technologies for fabrication of carbon nanotube-based
devices and circuits will eventually pave the way for electronics revolution in the molecular or nanoscale.
GLOSSARY
ACKNOWLEDGMENT
This work was sponsored by the National Science Foundation under the Materials Research Science and Engineering
Center program (DMR-9809686).
Nanotubes for Nanoelectronics
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
S. Iijima, Nature 354, 56 (1991).
C. Dekker, Phys. Today 22 (May 1999).
P. M. Ajayan, Chem. Rev. 99, 1787 (1999).
M. S. Dresselhaus, G. Dresselhaus, and P. C. Eklund, “Science of
Fullerenes and Carbon Nanotubes.” Academic Press, San Diego,
1995.
R Saito, M. S. Dresselhaus, and G. Dresselhaus, “Physical Properties of Carbon Nanotubes.” World Scientific, New York, 1998.
K. Tanaka, T. Yamabe, and K. Fukui, “The Science and Technology
of Carbon Nanotubes.” Elsevier, Oxford, 1999.
M. S. Dresselhaus, G. Dresselhaus, and Ph. Avouris, “Carbon
Nanotubes.” Springer-Verlag, Berlin, 2000.
J. W. Mintmire, B. I. Dunlap, and C. T. White, Phys. Rev. Lett. 68,
631 (1992).
N. Hamada, S.-I Sawada, and A. Oshiyama, Phys. Rev. Lett. 68,
1579 (1992).
R. Saito, M. Fujita, G. Dresselhaus, and M. S. Dresselhaus, Appl.
Phys. Lett. 60, 2204 (1992).
S. Iijima and T. Ichibashi, Nature 363, 603 (1993).
D. S. Bethune, C. H. Kiang, M. S. DeVries, G. Gorman, R. Savoy,
and R. Beyers, Nature 363, 605 (1993).
R. E. Smalley, http://www.ruf.rice.edu/∼smalleyg/image_gallery.
htm, 2002.
National Science and Technology Council, “National Nanotechnology Initiatrive: Leading to the Next Industrial Revolution,”
Washington, DC, 2000.
I. M. Ross, Proc. IEEE 86, 7 (1998).
J. S. Kilby, IEEE Trans. Electron Dev. ED-23, 648 (1976).
G. Binig, H. Roher, Ch. Gerber, and E. Weibel, Phys. Rev. Lett.
49, 57 (1982).
D. M. Eigler and E. K. Schweizer, Nature 344, 524 (1990).
M. F. Crommie, C. P. Lutz, and D. M. Eigler, Science 262, 218
(1993).
M. A. McCord and R. F. W. Pease, J. Vac. Sci. Technol. B 6, 293
(1988).
E. S. Snow, P. M. Campbell, and F. K. Perkins, Proc. IEEE 85, 601
(1997).
L. Stockman, G. Neuttiens, C. Van Haesendonck, and Y. Bruynseraede, Appl. Phys. Lett. 62, 2935 (1993).
A. L. DeLozanne, E. E. Ehrichs, and W. F. Smith, J. Phys.: Condens. Matter. 5, A409 (1993).
M. Wendel, S. Kuhn, H. Lorez, J. P. Kotthaus, and M. Holland,
Appl. Phys. Lett. 65, 1775 (1994).
J. W. Lyding, T.-C. Shen, J. S. Hubacek, J. R. Tucker, and G. C.
Abeln, Appl. Phys. Lett. 64, 2010 (1994).
J. E. Lilienfield, U.S. Patent 1, 745, 175, 1930.
O. Heil, British Patent 439457, 1935.
D. Kahng, IEEE Trans. Electron Dev. ED-23, 655 (1976).
P. S. Peercy, Nature 406, 1023 (2000).
J. D. Plummer and P. B. Griffin, Proc. IEEE 89, 240 (2001).
Semiconductor Industry Association (SIA), “International Technology Roadmap for Semiconductors,” San Jose, CA, 2001.
Y. Taur, IBM J. Res. Dev. 46, 213 (2002).
H.-S. P. Wong, IBM J. Res. Dev. 46, 133 (2002).
D. J. Frank, R. H. Dennard, E. Nowark, P. M. Solomon, Y. Taur,
and H.-S. P. Wong, Proc. IEEE 89, 259 (2001).
C. J. Gorter, Physica (Amsterdam) 17, 777 (1951).
T. A. Fulton and G. J. Dolan, Phys. Rev. Lett. 59, 109 (1987).
K. K. Likharev, IBM J. Res. Dev. 32, 144 (1988).
K. K. Likharev, Proc. IEEE 87, 606 (1999).
H. Ahmed, J. Vac. Sci. Technol. B 15, 2101 (1997).
D. Goldhaber-Gordon, M. S. Montemerlo, J. C. Love, G. J.
Opiteck, and J. C. Ellenbogen, Proc. IEEE 85, 521 (1997).
W. Chen, H. Ahmed, and K. Nakazato, Appl. Phys. Lett. 66, 3383
(1995).
939
21
42. D. L. Klein, P. L. McEuen, J. E. B. Katari, R. Roth, and A. P.
Alivisatos, Appl. Phys. Lett. 68, 2574 (1996).
43. Y. Nakamura, C. D. Chen, and J. S. Tsai, Japan J. Appl. Phys. 35,
L1465 (1996).
44. J.-I. Shirakashi, K. Matzumoto, N. Miura, and M. Konagai, Appl.
Phys. Lett. 72, 1893 (1998).
45. U. Meirav, M. A. Kastner, and S. J. Wind, Phys. Rev. Lett. 65, 771
(1990).
46. D. Ali and H. Ahmed, Appl. Phys. Lett. 64, 2119 (1994).
47. E. Leobandung, L. Guo, Y. Wang, and S. Y. Chou, Appl. Phys.
Lett. 67, 938 (1995).
48. Y. Takahashi, M. Nagase, H. Namatsu, K. Kuihara, K. Iwadate,
Y. Nakajima, S. Horiguchi, K. Murase, and M. Tabe, Electron Lett.
31, 136 (1995).
49. K. Kurihara, H. Namatsu, M. Nagase, and T. Takino, Microelectron.
Eng. 35, 261 (1997).
50. L. Zhuang, L. Guo, and S. Y. Chou, Appl. Phys. Lett. 72, 1205
(1998).
51. L. Guo, E. Leobandung, and S. Y. Chou, Science 275, 649 (1997).
52. R. Smith and H. Ahmed, J. Appl. Phys. 81, 6 (1997).
53. K. Saito, F. A. Williams, and A. S. Gordon, Combustion Sci. Technol. 47, 117 (1986).
54. K. Saito, F. A. Williams, W. F. Stickle, and A. S. Gordon, in “Proceedings of 20th Fall Technical Meeting,” Eastern Section, The
Combustion Institute, Gaithersburg, MD, 1987.
55. K. Saito, private communication.
56. L. Yuan, K. Saito, C. Pan, F. A. Williams, and A. S. Gordon, Chem.
Phys. Lett. 340, 237 (2001).
57. L. Yuan, K. Saito, W. Hu, and Z. Chen, Chem. Phys. Lett. 346, 23
(2001).
58. T. Guo, P. Nikolaev, A. Thess, D. T. Colbert, and R. E. Smalley.
Chem. Phys. Lett. 243, 49 (1995).
59. T. Guo and R. E. Smalley, in “Recent Advances in the Chemistry
and Physics of Fullerenes and Related Materials” (R. S. Ruoff
and K. M. Kadish, Eds.), p. 626. The Electrochemical Society,
Pennington, NJ, 1995.
60. A. Thess, R. Lee, P. Nikolaev, H. J. Dai, P. Petit, J. Robert, C. H.
Xu, Y. H. Lee, S. G. Kim, A. G. Rinzler, D. T. Colbert, G. E.
Scuseria, D. Tomanek, J. E. Fischer, and R. E. Smalley, Science
273, 483 (1996).
61. J. Kong, A. Cassell, and H. Dai, Chem. Phys. Lett. 292, 567 (1998).
62. A. Cassell, J. Raymakers, J. Kong, and H. Dai, J. Phys. Chem. 103,
6484 (1999).
63. J. Kong, H. T. Soh, A. Cassell, C. F. Quate, and H. Dai, Nature
395, 878 (1998).
64. R. Saito, M. Fujita, G. Dresselhaus, and M. S. Dresselhaus, Phys.
Rev. B 46, 1804 (1992).
65. J. W. G. Wildoer, L. C. Venema, A. G. Rinzler, R. E. Smalley, and
C. Dekker, Nature 391, 59 (1998).
66. M. S. Dresshaus, Nature 391, 19 (1998).
67. T. W. Odom, J.-L. Huang, P. Kim, and C. M. Lieber, Nature 391,
62 (1998).
68. J. A. Stroscio, R. M. Freenstra, and A. P. Fein, Phys. Rev. Lett. 57,
2579 (1986).
69. N. D. Lang, Phys. Rev. B 34, R5947 (1986).
70. A. M. Rao, P. C. Eklund, S. Bandow, A. Thess, and R. E. Smalley,
Nature 388, 257 (1997).
71. A. M. Rao, E. Richter, S. Bandow, B. Chase, P. C. Eklund, K. A.
Williams, S. Fang, K. R. Subbaswamy, M. Menon, A. Thess, R. E.
Smalley, G. Dresselhaus, and M. S. Dresselhaus, Science 275, 187
(1997).
72. J. E. Fischer, H. Dai, A. Thess, R. Lee, N. M. Hanjani, D. L.
Dehaas, and R. E. Smalley, Phys. Rev. B 55, R4921 (1997).
73. P. Petit, E. Jouguelet, J. E. Fischer, A. G. Rinzler, and R. E. Smalley, Phys. Rev. B 56, 9275 (1997).
74. T. Pichler, M. Knupfer, M. S. Golden, J. Fink, A. Rinzler, and
R. E. Smalley, Phys. Rev. Lett. 80, 4729 (1998).
940
22
75. J.-C. Charlier and Ph. Lambin, Phys. Rev. B 57, R15037 (1998).
76. J.-C. Charlie and J.-P. Issi, Appl. Phys. A 67, 79 (1998).
77. M. J. O’Connell, S. M. Bachilo, C. B. Huffman, V. C. Moore,
M. S. Strano, E. H. Haroz, K. L. Rialon, P. J. Boul, W. H. Noon,
C. Kittrell, J. Ma, R. H. Hauge, R. B. Weisman, and R. E. Smalley,
Science 297, 593 (2002).
78. P. Delaney, H. J. Choi, J. Lhm, S. G. Louie, and M. L. Cohen,
Nature 391, 466 (1998).
79. S. G. Lemay, J. G. Janssen, M. van den Hout, M. Mooij, M. J.
Bronlkowski, P. A. Willis, R. E. Smalley, L. P. Kouwenhoven, and
C. Dekker, Nature 412, 617 (2001).
80. L. Langer, L. Stockman, J. P. Heremans, V. Bayot, C. H. Olk,
C. Van Haesendonck, Y. Bruynseraede, and J.-P. Issi, J. Mater. Res.
9, 927 (1994).
81. W. A. de Heer, A. Chatelain, and D. Ugarte, Science 270, 1179
(1995).
82. L. Langer, V. Bayot, E. Grivei, J.-P. Issi, J. P. Heremans,, C. H.
Olk, L. Stockman, C. Van Haesendonck, and Y. Bruynseraede,
Phys. Rev. Lett. 76, 479 (1996).
83. H. Dai, E. W. Wong, and C. M. Lieber, Science 272, 523 (1996).
84. T. W. Ebbesen H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff,
Nature 391, 667 (1996).
85. M. Bockrath, D. H. Cobden, P. L. McEuen, N. G. Chopra,
A. Zettl, A. Thess, and R. E. Smalley, Science 275, 1922 (1997).
86. S. J. Tans, M. H. Devoret, H. Dai, A. Thess, R. E. Smalley, L. J.
Geerligs, and C. Dekker, Nature 386, 474 (1997).
87. L. Chico, L. X. Benedict, S. G. Louie, and M. L. Cohen, Phys. Rev.
B 54, 2600 (1996).
88. C. Roland, M. B. Nardelli, H. Guo, H. Mehrez, J. Taylor, J. Wang,
and Y. Wei, Surf. Rev. Lett. 7, 637 (2000).
89. W. Tian and S. Datta, Phys. Rev. B 49, 5097 (1994).
90. M. F. Lin and K.-W.-K. Shung, Phys. Rev. B 51, 7592 (1995).
91. S. Frank, P. Poncharal, Z. L. Wang, and W. A. de Heer, Science
280, 1744 (1998).
92. J. Kong, E. Yenilmez, T. W. Tonbler, W. Kim, H. Dai, R. B. Laughlin, L. Liu, C. S. Jayanthi, and S. Y. Wu, Phys. Rev. Lett. 87, 106801
(2001).
93. C. T. White and T. N. Todorov, Nature 393, 240 (1998).
94. J. W. Park, J. Kim, J.-O. Lee, K.-C. Kang, J.-J. Kim, and K.-H.
Yoo, Appl. Phys. Lett. 80, 133 (2002).
95. V. H. Crespi, A. M. L. Cohen, and A. Rubio, Phys. Rev. Lett. 79,
2093 (1997).
96. M. P. Anantram and T. R. Govindan, Phys. Rev. B 58, 4882 (1998).
97. T. Kostyrko, M. Bartkowiak, and G. D. Mahan, Phys. Rev. B 59,
3241 (1999).
98. T. Ando, T. Nakanishi, and R. Saito, J. Phys. Soc. Jpn. 67, 2857
(1998).
99. T. Ando, Semicond. Sci. Technol. 15, R13 (2000).
100. P. L. McEuen, M. Bockrath, D. Cobden, Y. G. Yoon, and S. Louie,
Phys. Rev. Lett. 83, 5098 (1999).
101. S. Roche, F. Triozon, and A. Rubio, Appl. Phys. Lett. 79, 3690
(2001).
102. S. J. Tans, M. H. Devoret, R. J. A. Groeneveld, and C. Dekkers,
Nature 397, 673 (1999).
103. D. H. Cobden, M. Bockrath, P. L. McEuen, A. G. Rinzler, and
R. E. Smalley, Phys. Rev. Lett. 81, 681 (1998).
104. D. H. Cobden, M. Bockrath, N. G. Chopra, A. Zettle, P. L.
McEuen, A. G. Rinzler, A. Thesis, and R. E. Smalley, Physica B
251, 132 (1998).
105. Y. Aharonove and D. Bohm, Phys. Rev. 115, 485 (1959).
106. W. Tian and S. Data, Phys. Rev. B 49, 5097 (1994).
107. A. Bachtold, C. Strunk, J.-P. Salvetat, J.-M. Bonard, L. Forro,
T. Nussbaumer, and C. Schonenberger, Nature 397, 673 (1999).
108. S. J. Tans, M. H. Devoret, R. J. A. Groeneveld, and C. Dekker,
Nature 394, 761 (1998).
109. M. P. A. Fisher and P. A. Glazman, “A Mesoscopic Electron Transport.” Kluwer Academic, Boston, 1997.
Nanotubes for Nanoelectronics
110. C. Kane, L. Balents, and M. P. A. Fisher, Phys. Rev. Lett. 79, 5086
(1997).
111. R. Egger and A. O. Gogolin, Phys. Rev. Lett. 79, 5082 (1997).
112. R. Egger, Phys. Rev. Lett. 83, 5547 (1999).
113. M. Bockrath, D. H. Cobden, J. Lu, A. G. Rinzler, R. E. Smalley,
L. Balents, and P. L. McEuen, Nature 397, 598 (1999).
114. J. Kong, C. Zhou, E. Yenilmez, and H. Dai, Appl. Phys. Lett. 77,
3977 (2000).
115. J. Kong, J. Cao, and H. Dai, Appl. Phys. Lett. 80, 73 (2002).
116. H. W. Ch. Postma, M. de Jonge, Z. Yao, and C. Dekker, Phys. Rev.
B 62, R10653 (2000).
117. H. W. Ch. Postma, A. Sellmeijer, and C. Dekker, Adv. Mater. 17,
1299 (2000).
118. H. W. Ch. Postma, T. Teepen, Z. Yao, and C. Dekker, Science 293,
76 (2001).
119. J. B. Cui, M. Burghard, and K. Kern, Nano Lett. 2, 117 (2002).
120. J. W. Park, J. B. Choi, and K. H. Yoo, Appl. Phys. Lett. 81, 2644
(2002).
121. K. Ishibashi, M. Suzuki, T. Ida, and Y. Aoyagi, Appl. Phys. Lett.
79, 1864 (2001).
122. J. Nygard and D. H. Cobden, Appl. Phys. Lett. 79, 4216 (2001).
123. J. Park and P. L. McEuen, Appl. Phys. Lett. 79, 1363 (2001).
124. D. Bozovic and M. Bockrath, Appl. Phys. Lett. 78, 3693 (2001).
125. K. Ishibashi, M. Suzuki, T. Ida, and Y. Aoyagi, Appl. Phys. Lett.
80, 4238 (2002).
126. P. G. Collins, A. Zettle, H. Bando, A. Thess, and R. E. Smalley,
Science 278, 100 (1997).
127. L. Roschier, J. Penttila, M. Martin, P. Hakonen, M. Paalanen,
U. Tapper, E. I. Kauppinen, C. Journet, and P. Bernier, Appl. Phys.
Lett. 75, 728 (1999).
128. L. Roschier, R. Tarkiainen, M. Ashlskog, M. Paalanen, and
P. Hakonen, Appl. Phys. Lett. 78, 3295 (2001).
129. W. B. Choi, J. U. Chu, K. S. Jeong, E. J. Bae, and J.-W. Lee, Appl.
Phys. Lett. 79, 3696 (2001).
130. M. Suzuki, K. Ishibashi, K. Toratani, D. Tsuya, and Y. Aoyagi,
Appl. Phys. Lett. 81, 2273 (2002).
131. M. Ashlog, R. Tarkiainen, L. Roschier, and P. Hakonen, Appl.
Phys. Lett. 77, 4307 (2000).
132. A. Kanda, Y. Ootuka, K. Tsukagoshi, and Y. Aoyagi, Appl. Phys.
Lett. 79, 1354 (2001).
133. R. J. Schoelkopf, P. Wahlgren, A. A. Kozhevnikov, P. Selsing, and
D. E. Prober, Science 280, 1238 (1998).
134. P. G. Collins, M. S. Fuhrer, and A. Zettle, Appl. Phys. Lett. 76, 894
(2000).
135. H. Ouacha, M. Willander, H. Y. Yu, Y. W. Park, M. S. Kabir,
S. H. M. Persson, L. B. Kish, and A. Ouacha, Appl. Phys. Lett. 80,
1055 (2002).
136. S. J. Tans, A. R. M. Verschueren, and C. Dekker, Nature 393, 49
(1998).
137. R. Martel, T. Schmidt, H. R. Shea, T. Hertel, and Ph. Avouris,
Appl. Phys. Lett. 73, 2447 (1998).
138. P. Avouris, T. Hertel, R. Martel, T. Schmidt, H. Shea, and
R. Walkup, Appl. Surf. Sci. 141, 201 (1999).
139. P. Avouris, Chem. Phys. 281, 429 (2002).
140. P. G. Collins and P. Avouris, Sci. Am. 62 (2000).
141. H. Dai, J. Kong, C. Zhou, N. Franklin, T. Tombler, A. Cassell,
S. Fan, and M. Chapline, J. Phys. Chem. B 103, 11246 (1999).
142. J. Guo, M. Lundstrom, and S. Datta, Appl. Phys. Lett. 80, 3192
(2002).
143. A. Rochefort, M. Di Ventra, and Ph. Avouris, Appl. Phys. Lett. 78,
2521 (2001).
144. S. J. Wind, J. Appenzeller, R. Martel, V. Derycke, and Ph. Avouris,
Appl. Phys. Lett. 80, 3817 (2002).
145. B. Yu, in “Proc. Int. Electron Dev. Meet.,” IEEE Electron Device
Society, 2001, p. 937.
146. R. Chau, in “Proc. Int. Electron Dev. Meet.,” IEEE Electron
Device Society, 2001, p. 621.
Nanotubes for Nanoelectronics
147. R. S. Muller and T. I. Kamins, “Device Electronics for Integrated
Circuits.” Wiley, New York, 1986.
148. C. Bena, S. Vishveshwara, L. Balents, and M. P. A. Fisher, Phys.
Rev. Lett. 89, 37901 (2002).
149. S. Rosenblat, Y. Yaish, J. Park, J. Gore, V. Sazonova, and P. L.
McEuen, Nano Lett. 2, 869 (2002).
150. M. Kruger, M. R. Buitelaar, T. Nussbaumer, C. Schnenberger, and
L. Forro, Appl. Phys. Lett. 78, 1291 (2001).
151. S. Kazaoui, N. Minami, N. Matsuda, H. H. Kataura, and
Y. Achiba, Appl. Phys. Lett. 78, 3433 (2001).
152. M. S. Fuhrer, B. M. Kim, T. Durkop, and T. Brintlinger, Nano Lett.
2, 755 (2002).
153. K. Liu, M. Burghard, and S. Roth, Appl. Phys. Lett. 75, 2494 (1999).
154. T. W. Tombler, C. Zhou, J. Kong, and H. Dai, Appl. Phys. Lett. 76,
2412 (2000).
155. Y. H. Kim and K. J. Cheng, Appl. Phys. Lett. 81, 2264 (2002).
156. A. Javey, M. Shim, and H. Dai, Appl. Phys. Lett. 80, 1064 (2002).
157. C. Zhou, J. Kong, and H. Dai, Appl. Phys. Lett. 76, 1597 (2000).
158. J. O’Keeffe, C. Wei, and K. Cho, Appl. Phys. Lett. 80, 676 (2002).
159. J. Guo, S. Goasguen, M. Lundstrom, and S. Datta, Appl. Phys.
Lett. 81, 1486 (2002).
160. A. Bachtold, P. Hadley, T. Nakanishi, and C. Dekker, Science 294,
1317 (2001).
161. V. Derycke, R. Martel, J. Appenzeller, and Ph. Avouris, Nano Lett.
1, 453 (2001).
162. X. Liu, C. Lee, and C. Zhou, Appl. Phys. Lett. 79, 3329 (2001).
163. T. Rueckes, K. Kim, E. Joselevich, G. Y. Tseng, C.-L. Cheung, and
C. M. Lieber, Science 289, 94 (2000).
164. M. Radosavljevic, M. Fretag, K. V. Thadani, and A. T. Johson,
Nano Lett. 2, 761 (2002).
165. J. B. Cui, R. Sordan, M. Burghard, and K. Kern, Appl. Phys. Lett.
81, 3260 (2002).
166. N. Yoneya, K. Tsukagoshi, and Y. Aoyagi, Appl. Phys. Lett. 81,
2250 (2002).
167. R. D. Antonov and A. T. Johnson, Phys. Rev. Lett. 83, 3274 (1999).
168. R. S. Lee, H. J. Kim, J. E. Fischer, J. Lefebvre, M. Radosavljevic,
J. Hone, and A. T. Johnson, Phys. Rev. B 61, 4526 (2000).
169. M. Bockrath, J. Hone, A. Zettle, P. L. McEuen, A. G. Rinzler,
and R. E. Smalley, Phys. Rev. B 61, R10606 (2000).
170. J. Kong, C. Zhou, E. Yenilmez, and H. Dai, Appl. Phys. Lett. 77,
3977 (2000).
171. V. Derycke, R. Martel, J. Appenzeller, and Ph. Avouris, Appl. Phys.
Lett. 80, 2773 (2002).
172. Z. Yao, H. W. Ch. Postma, L. Balents, and C. Dekker, Nature 402,
273 (1999).
173. A. N. Andriotis, M. Menon, D. Srivastava, and L. Chernozatonskii,
Phys. Rev. Lett. 87, 66802 (2001).
174. B. Wei, R. Spolenak, P. Kohler-Redlich, M. Ruhle, and E. Arzt,
Appl. Phys. Lett. 74, 3149 (1999).
175. R. Pati, Y. Zhang, and S. K. Nayak, Appl. Phys. Lett. 81, 2638
(2002).
176. C. Zhou, J. Kong, E. Yenilmez, and H. Dai, Science 290, 1552
(2000).
177. L. Chico, V. H. Crespi, L. X. Benedict, S. G. Louie, and M. L.
Cohen, Phys. Rev. Lett. 76, 971 (1996).
178. J. Han, M. P. Anantram, R. L. Jaffe, J. Kong, and H. Dai, Phys.
Rev. B 57, 14983 (1998).
179. J.-O. Lee, H. Oh, J.-R. Kim, K. Kang, J.-J. Kim, J. Kim, and K.-H.
Yoo, Appl. Phys. Lett. 79, 1351 (2001).
180. G. W. Ho, A. T. S. Wee, and J. Lin, Appl. Phys. Lett. 79, 260 (2001).
181. X. Ma and E. G. Wang, Appl. Phys. Lett. 78, 978 (2001).
182. M. S. Fuhrer, J. Nygard, L. Shih, M. Forero, Y.-G. Yoon, M. S. C.
Mazzoni, H. J. Choi, J. Ihm, S. G. Loie, A. Zettle, and P. L.
McEuen, Science 288, 494 (2000).
183. F. Leonard and J. Tersoff, Phys. Rev. Lett. 85, 4767 (2000).
184. T. Yamada, Appl. Phys. Lett. 80, 4027 (2002).
185. A. A. Odintsov, Phys. Rev. Lett. 85, 150 (2000).
941
23
186. G. D. J. Smit, S. Rogge, and T. M. Klapwijk, Appl. Phys. Lett. 81,
3852 (2002).
187. M. Menon and D. S. Srivastava, Phys. Rev. Lett. 79, 4453 (1997).
188. J. Li, C. Papadopoulos, and J. Xu, Nature 402, 254 (1999).
189. C. Papadopoulos, A. Rakitin, J. Li, A. S. Vedeneev, and J. M. Xu,
Phys. Rev. Lett. 85, 3476 (2000).
190. B. C. Satishkumar, P. J. Thomas, A. Govindaraj, and C. N. R. Rao,
Appl. Phys. Lett. 77, 2530 (2000).
191. D. Zhou and S. Seraphin, Chem. Phys. Lett. 238, 286 (1995).
192. B. Gan, J. Ahn, A. Zhang, S. F. Yoon, Q. F. Huang, H. Yang, M. B.
Yu, and W. Z. Li, Diamond Relat. Mater. 9, 897 (2000).
193. J. M. Ting and C.-C. Chang, Appl. Phys. Lett. 80, 324 (2002).
194. B. Gan, J. Ahn, Q. Zhang, Q.-F. Huang, C. Kerlit, S. F. Yoon,
Rusli, V. A. Ligachev, X.-B. Zhang, and W.-Z. Li, Mater. Lett. 45,
315 (2000).
195. W. Z. Li, J. G. Wen, and Z. F. Ren, Appl. Phys. Lett. 79, 1879
(2001).
196. P. Nagy, R. Ehlich, L. P. Biro, and J. Gyulai, Appl. Phys. A 70, 481
(2000).
197. A. N. Andriotis, M. Menon, D. Srivastva, and L. Chernozatonskii,
Phys. Rev. Lett. 87, 66802 (2001).
198. A. N. Andriotis, M. Menon, D. Srivastva, and L. Chernozatonskii,
Appl. Phys. Lett. 79, 266 (2001).
199. M. Menon and D. Srivastva, J. Mater. Res. 13, 2357 (1998).
200. M. Freitag, M. Radosavljevic, Y. Zhou, and A. T. John, Appl. Phys.
Lett. 79, 3326 (2001)
201. Y. Zhang, T. Ichihashi, E. Landree, F. Nihey, and S. Iijima, Science
285, 1719 (1999).
202. J. Appenzeller, R. Martel, P. Avouris, H. Stahl, and B. Lengeler,
Appl. Phys. Lett. 78, 3313 (2001).
203. H. T. Soh, C. F. Quate, A. F. Morpurgo, C. M. Marcus, J. Kong,
and H. Dai, Appl. Phys. Lett. 75, 627 (1999).
204. J. Lefebvre, J. F. Lynch, M. Llaguno, M. Radosavljevic, and A. T.
Johnson, Appl. Phys. Lett. 75, 3014 (1999).
205. P. G. Collins, M. S. Arnold, and P. Avouris, Science 292, 706 (2000).
206. T. Hertel, R. Martel, and P. Avouris, J. Phys. Chem. B 102, 910
(1998).
207. L. C. Venema, J. W. G. Wildoer, H. L. J. T. Tuinstra, C. Dekker,
A. G. Rinzler, and R. E. Smalley, Appl. Phys. Lett. 71, 2629 (1997).
208. A. Bachtold, M. S. Fuhrer, S. Plyasunov, M. Forero, E. H. Anderson, A. Zettle, and P. L. McEuen, Phys. Rev. Lett. 84, 6082 (2000).
209. M. Bockrath, W. Liang, D. Bozovic, J. H. Hafner, C. M. Lieber,
M. Tinkham, and H. Park, Science 291, 283 (2001).
210. S. J. Tans and C. Dekker, Nature 404, 834 (2000).
211. M. R. Falvo, R. M. Taylor II, A. Helser, V. Chi, F. P. Brooks, Jr.,
S. Washburn, and R. Superfine, Nature 397, 236 (1997).
212. M. R. Falvo, G. J. Clary, R. M. Taylor II, V. Chi, F. P. Brooks, Jr.,
S. Washburn, and R. Superfine, Nature 389, 582 (1997).
213. D. Bozovic, M. Bockath, J. H. Halfner, C. M. Lieber, H. Park, and
M. Tinkam, Appl. Phys. Lett. 78, 3693 (2001).
214. C. Thelander, M. H. Magnusson, K. Deppert, L. Samuelson, P. R.
Poulsen, J. Nygard, and J. Borgreen, Appl. Phys. Lett. 78, 3693
(2001).
215. P. A. Williams, S. J. Padakis, M. R. Falvo, A. M. Patel, M. Sinclair, A. Seeger, A. Helser, R. M. Taylor II, S. Washburn, and
R. Superfine, Appl. Phys. Lett. 80, 2574 (2002).
216. J.-Y. Park, Y. Taish, M. Brink, S. Rosenblatt, and P. L. McEuen,
Appl. Phys. Lett. 80, 4446 (2002).
217. T. W. Thombler, C. Zhou, L. Alexseyev, J. Kong, H. Dai, L. Liu,
C. S. Jayanthi, M. Tang, and S.-Y. Wu, Nature 405, 769 (2000).
218. L. Liu, C. S. Jayanthi, M. Tang, S. Y. Wu, T. W. Tombler, C. Zhou,
L. Alexseyev, J. Kong, and H. Dai, Phys. Rev. Lett. 84, 4950 (2000).
219. L. Liu, C. S. Jayanthi, and S. Y. Wu, Phys. Rev. B 64, 33412 (2001).
220. H. Watanabe, C. Manabe, T. Shigematsu, and M. Shimizu, Appl.
Phys. Lett. 78, 2928 (2001).
221. H. Hirayama, Y. Kawamoto, Y. Ohshima, and K. Takayanagi,
Appl. Phys. Lett. 79, 1169 (2001).
942
24
222. P. J. de Pablo, C. Gomez-Navarro, A. Gil, J. Colchero, M. T. Martinez, A. M. Benito, W. K. Maser, J. Gomez-Herrero, and A. M.
Baro, Appl. Phys. Lett. 79, 2979 (2001).
223. S. Akita, Y. Nakayama, S. Mizooka, Y. Takano, T. Okawa, Y. Miyatake, S. Yamanaka, M. Tsuji, and T. Nosaka, Appl. Phys. Lett. 79,
1691 (2001).
224. B. Q. Wei, R. Vajtai, and P. M. Ajayan, Appl. Phys. Lett. 79, 1172
(2001).
225. W. Z. Li, S. S. Xie, L. X. Qian, B. H. Chang, B. S. Zou, W. Y.
Zhou, R. A. Zhao, and G. Wang, Science 274, 1701 (1996).
226. W. Z. Li, H. Zhang, C. Wang, Y. Zhang, L. Xu, K. Zhu, and S. Xie,
Appl. Phys. Lett. 70, 2684 (1997).
227. D. Xu, G. Guo, L. Gui, Y. Tang, Z. Shi, Z. Jin, Z. Gu, W. Liu,
X. Li, and G. Zhang, Appl. Phys. Lett. 75, 481 (1999).
228. Z. F. Ren, Z. P. Huang, J. W. Xu, J. H. Wang, P. Bush, M. P. Siegal,
and P. N. Provencio, Science 282, 1105 (1998).
229. Z. F. Ren, Z. P. Huang, D. Z. Wang, J. G. Wen, J. W. Xu, J. H.
Wang, L. E. Calvet, J. Chen, J. F. Klemic, and M. A. Reed, Appl.
Phys. Lett. 75, 1086 (1999).
230. M. P. Siegal, D. L. Overmyer, and P. P. Provencio, Appl. Phys. Lett.
80, 2171 (2001).
231. S. Fan, W. Liang, H. Dang, N. Franklin, T. Tombler, M. Chapline,
and H. Dai, Physica E 8, 179 (2000).
232. G. C. Wood and J. P. O’Sullivan, J. Electrochem. Soc. 116, 1351
(1969).
233. O. Jessensky, F. Muller, and U. Gosele, J. Electrochem. Soc. 145,
3735 (1998).
234. H. Masuda and K. Fukuda, Science 268, 1466 (1995).
235. J. Li, M. Moskovits, and T. L. Haslett, Chem. Mater. 10, 1963
(1998).
236. J. Li, C. Papadopoulos, J. M. Xu, and M. Moskovits, Appl. Phys.
Lett. 75, 367 (1999).
237. J. S. Suh and J. S. Lee, Appl. Phys. Lett. 75, 2047 (1999).
238. J. S. Suh, K. S. Jeong, J. S. Lee, and I. Han, Appl. Phys. Lett. 80,
2392 (2002).
239. S. L. Sung, S. H. Tsai, C. H. Tseng, F. K. Chiang, X. W. Liu, and
H. C. Shih, Appl. Phys. Lett. 74, 197 (1999).
240. S.-H. Jeong, O.-J. Lee, K.-H. Lee, S. H. Oh, and C.-G. Park,
Chem. Mater. 14, 1859 (2002).
241. Z. H. Yuan, H. Huang, H. Y. Dang, J. E. Cao, B. H. Hu, and S. S.
Fan, Appl. Phys. Lett. 78, 3127 (2001).
Nanotubes for Nanoelectronics
242. T. Iwasaki, T. Motoi, and T. Den, Appl. Phys. Lett. 75, 2044 (1999).
243. W. C. Hu, L. M. Yuan, Z. Chen, D. W. Gong, and K. Saito,
J. Nanosci. Nanotechnol. 2, 203 (2002).
244. W. C. Hu, D. W. Gong, Z. Chen, L. M. Yuan, K. Saito, P. Kichambare, and C. A. Grimes, Appl. Phys. Lett. 79, 3083 (2001).
245. M. Terrones, N. Grobert, J. Olivares, J. P. Zhang, H. Terrones,
K. Kordaros, W. K. Hsu, J. P. Hare, P. D. Towbsend, K. Prassides,
A. K. Cheetham, H. W. Kroto, and D. R. M. Walto, Nature 388,
52 (1997).
246. H. Dai, Phys. World 43 (2000).
247. H. Dai, J. Kong, C. Zhou, N. Franklin, T. Tombler, A. Cassell,
S. Fan, and M. Chapline, J. Phys. Chem. 103s, 11246 (1999).
248. A. M. Cassell, R. Franklin, T. W. Tombler, E. M. Chan, J. Han,
and H. Dai, J. Am. Chem. Soc. 121, 7975 (1999).
249. N. R. Franklin and H. Dai, Adv. Mater. 12, 890 (2000).
250. N. R. Franklin, Y. Li, R. J. Chen, A. Javey, and H. Dai, Appl.
Phys. Lett. 79, 4571 (2001).
251. N. R. Franklin, Q. Wang, T. W. Tombler, A. Javey, and M. Shim,
Appl. Phys. Lett. 81, 913 (2002).
252. Y. Zhang, A. Chang, J. Cao, Q. Wang, W. Kim, Y. Li, N. Morris, E. Yenilmez, J. Kong, and H. Dai, Appl. Phys. Lett. 79, 3155
(2001).
253. A. Ural, Y. Li, and H. Dai, Appl. Phys. Lett. 81, 3464 (2002).
254. Y. Avigal and R. Kalish, Appl. Phys. Lett. 78, 2291 (2001).
255. Y. Homma, Y. Kobayashi, and T. Ogino, Appl. Phys. Lett. 81, 2261
(2002).
256. N. Chopra, P. D. Kichamare, R. Andrews, and B. J. Hinds, Nano
Lett. 2, 1177 (2002).
257. J. C. Lewenstein, T. P. Burgin, A. Ribayrol, L. A. Nagahara, and
R. K. Tsui, Nano Lett. 2, 443 (2002).
258. X. Q. Chen, T. Saito, H. Yamada, and K. Matsushige, Appl. Phys.
Lett. 78, 3714 (2001).
259. H. Dai, N. Franklin, and J. Han, Appl. Phys. Lett. 73, 1508 (1998).
260. J. Lefebvre, M. Radosavljevic, and A. T. Johnson, Appl. Phys. Lett.
76, 3828 (2000).
261. W. S. Yun, J. Kim, K.-H. Park, J. S. Ha, Y.-J. Ko, K. Park, S. K.
Kim, Y.-J. Doh, H.-J. Lee, J. P. Salvetat, and L. Forro, J. Vac. Sci.
Technol. A 18, 1329 (2000).
262. P. L. McEuen, Phys. World 31 (2000).
263. F. Kreupl, A. Graham, and W. Honlein, Solid State Technol. S9
(2002).